According to VisualThesaurus, John Heisman originated the term in the 1890s:
Back in the 1890s, John Heisman — of Heisman Trophy fame — introduced the word hike to football. Originally, the center (who puts the ball into play) used one hand to flip the ball under his legs to the quarterback. To alert the center that he was ready to start, a quarterback would use a touch signal, often scratching the center's leg. When playing as a center for the University of Pennsylvania team in 1890-91, Heisman got tricked by an opposing player who scratched his leg. He flipped the ball back, and the quarterback missed the pass. Heisman's solution was to have the quarterback use the word hike to put the ball into motion so that everyone was clear when the play started. Hike was a good choice, since it can mean "to pull or raise with a sudden motion," and that's what the center does with the ball.