Joe Falling Hawk was a Native American poker player in San Francisco in the 19th century and gambling partner to Frederick La Rouque, with whom he usually cooperated to fleece other players.

When Data traveled back to 1893, he wished to join a game to earn enough money to pay for a room, clothing, and parts for a triolic wave detector. Falling Hawk believed Data was an easy mark. However, Data apparently did so well that he won the clothes off the gamblers' backs. Data returned to his room wearing La Rocque's vest and Falling Hawk's bowler hat. (TNG: "Time's Arrow")

Joe Falling Hawk was played by Sheldon Peters Wolfchild.