Robinson was born in Monticello, Florida, the son of Johnnie Robinson, a truck driver, and his wife, Jean. He grew up in Tallahassee, where he played football with neighborhood kids from a very young age. He played high school football at Tallahassee's Leon High School under heralded coach Gene Cox. He joined Leon's junior varsity squad as a freshman in 1978, initially playing at wide receiver, but switching to quarterback when Cox noticed how easily he could throw the ball long distances.