Twelve-year-old Kevin Kim, a Korean American boy living in Dorchester, New York, is home alone on a Monday afternoon in February 1999, bored and avoiding his social-studies homework. While playing wall ball against his bedroom wall, he hears a loud thud. An arrow flies across the room, pierces the button on his baseball cap, and pins it to the wall. A man crouches behind Kevin's bed, armed with a bow and arrows. Kevin is terrified but observes the stranger: an Asian man in his twenties wearing white clothes, with long black hair and a quiver on his back. The man claims he fell off a tiger and landed in Kevin's room.
When Kevin explains that the man is in America, the stranger is baffled, insisting Kevin must be either Yemek or Chinese. Kevin clarifies he is Korean American. The man introduces himself as Koh Chu-mong, "Skillful Archer," and Kevin begins calling him "Archie" in his thoughts while addressing him as "Archer." Archie tries to demonstrate his skill by shooting at a neighbor's birdfeeder but shatters Kevin's bedroom window, having never encountered glass. As Kevin cleans up, Archie reveals that his father tried to kill him multiple times as an infant by placing him among wild animals, but each time the animals protected the baby. A fortuneteller had predicted his youngest son would become a great leader, and the father feared the boy would usurp the throne. Kevin discovers that Archie forbids questions from a younger person, so he develops a technique of phrasing questions as statements to draw out information.
Archie announces he must return home. Kevin uses a globe to show that Korea and America are on opposite sides of the world. Archie recognizes both China, where he was born, and his kingdom, Koguryo, an ancient Korean kingdom predating the nation of Korea by centuries. Kevin suggests that since Archie appeared by magic, he must return by magic. He leads Archie to the family computer, describing it as a "magic box" since Archie has no concept of technology. An online search confirms that Chu-mong was born in 55 B.C. and founded Koguryo in 37 B.C., revealing that Archie is from the ancient past. Kevin phones his paternal grandparents, Ah-jee and Ah-mee, who are originally from Korea. Ah-jee recalls Chu-mong's legendary archery and suggests Kevin contact Professor Lee, a curator of Asian collections at the local museum and an expert on Korean history.
Kevin decides to take Archie to the museum. On the street, Archie panics at a passing car, dragging Kevin through a thorny hedge and giving him a black eye. As they walk, Archie explains the Chinese zodiac, a system in which 12 animals and five elements (Fire, Earth, Metal, Water, Wood) rotate in overlapping cycles, and asks which element cycle Kevin was born under. Kevin attempts the math but gives up. Archie reveals he was born in the year of the Tiger during a Fire cycle, making him a Fire-tiger. He then notes a series of tiger connections: he was riding a tiger when he fell through time, it is currently a Tiger year, Kevin was also born in a Tiger year, and Kevin's family displays a university Tigers banner. Archie concludes these connections are the source of the magic that brought him here and grows alarmed upon learning the Tiger year ends that very day, insisting that Tiger magic only works during a Tiger year and that he has mere hours before he must wait 12 years for the next cycle.
At the museum, Kevin leaves Archie outside and examines the Korea exhibit but finds nothing relevant. He meets Professor Lee, who shares that Chu-mong was beloved by his people and is credited with introducing chopsticks to Korea. The professor notes that legends surround Chu-mong as they do King Arthur. Kevin nearly reveals Archie's presence but catches himself and abruptly leaves.
Discouraged, Kevin struggles to plan a next step. Archie teaches him a calming exercise: gathering all movement into an imaginary ball in his belly and pushing it down. With a clearer mind, Kevin identifies tigers as the most promising lead and decides to visit the city zoo. On the walk, Archie tells the story of his escape from his father's kingdom in the third person, to maintain modesty, describing how he fled with loyal friends, reached a raging river, and shot three arrows into the water. Dozens of turtles rose to form a living bridge that dissolved behind his party after they crossed.
At the zoo, Archie silently disappears. He retrieves his bow, climbs the exterior wall, and swings into the tiger enclosure on a rope-tethered arrow. He bows to the Bengal tiger and examines its coat before escaping with another rope technique. Archie explains that the tiger's thin coat indicates a warm-climate origin, not the cold mountains of Koguryo, so this tiger cannot transport him home.
Kevin takes Archie to the Jade Palace, a nearby Chinese restaurant. While Archie meditates, Kevin studies the zodiac placemat and revisits his earlier calculation. He determines that 2,040 years separate his birth from Archie's, accounting for the absence of a year 0 A.D. Dividing 2,040 by 12 gives 170 cycles, and dividing by 5 gives 34, meaning Kevin shares Archie's element cycle. Kevin announces he is also a Fire-tiger, but Archie responds calmly that he already suspected as much.
A waiter strikes a bronze gong for a birthday celebration. The metallic sound triggers a connection: there is a bronze tiger statue at the entrance to Dorchester State University. Archie is thrilled, explaining that because it is a Metal-tiger year in his own time, riding a metal tiger aligns with the magic for his return. As they leave, Archie declines Kevin's offer of chopsticks as a souvenir, explaining he must not carry anything from the future. He reflects that even his memory of the visit may not survive, but he hopes to retain an unconscious sense of what he has learned: that ordinary people can contribute to extraordinary missions.
Near the zoo, Professor Lee calls out from his car. He reveals he followed Kevin from the museum and witnessed Archie's stunt at the zoo. The professor presents two possibilities: either the man needs medical help, or he truly is the ancient Chu-mong, an unprecedented opportunity for study. Kevin recognizes that either option would trap Archie in the modern world and yells for Archie to run. A tractor-trailer jackknifes across Route 104, blocking traffic, and they dash across while Mr. Lee is stuck behind.
At the bronze tiger statue, Archie gives Kevin the two halves of an arrow broken during the zoo escape, saying Kevin is already worthy of the gift. He mounts the statue and feels magic vibrating in the air, but nothing happens. Mr. Lee arrives on foot, and Archie aims an arrow at the professor. Kevin steps in front of Mr. Lee, blocking the shot. Archie feels betrayed, but Kevin pleads with him to trust him one last time. Archie lowers his bow. Kevin closes his eyes and uses the stillness technique. The logic clicks: Archie's time is a Metal-tiger year, but Kevin's time is an Earth-tiger year. The missing element is earth itself. Kevin scrapes dirt from the base of the statue, shouts "EARTH," and flings the clods over Archie, who has remounted the tiger. Archie vanishes instantly. Kevin offers Mr. Lee the broken arrow for the museum, and the awestruck professor drives him home.
Life returns to normal. Kevin tells his parents a partial truth and lets his mother blame the broken window on his bouncy ball, believing Archie's visit was meant only for him. The following Saturday, Kevin asks his father for archery lessons. His grandfather reveals that Kevin's father was a Youth Champion archer at Kevin's age, a fact never shared because his father assumed Kevin would not be interested. Kevin's grandparents arrive with belated birthday presents: a new bow and arrows for Kevin and his father's old bow, cleaned and restrung. Kevin connects archery to math, recognizing both require precision and the certainty of knowing when a shot, or an answer, is right. When his father agrees to give him a lesson immediately, Kevin says they should start right away, signaling a new bond and a newfound commitment to discipline.