While the date of their introduction is uncertain, the fire arrows launched by gunpowder are considered to be the first true rockets. These fire arrows were traditional feathered arrows propelled by ignited gunpowder housed in a tube tied to the arrow.

Cliff Lethbridge, History of Rocketry: Ancient Times to the 17th Century, 2000

Singijeon or Shinkichon (magical machine arrows) was a type of Korean (Joseon) fire arrow rocket, used during the Joseon Dynasty (1392-1897). Multiple Singijeon could be launched by hwacha (multiple rocket launcher).

Singijeon, Wikipedia