Robinson played college football at the University of Tennessee from 1982 to 1985. After spending his first two seasons as a backup, he guided the 1984 squad to a 7–4–1 record and an appearance in the Sun Bowl. He led the 1985 "Sugar Vols" squad through a difficult first half of the season, and was a Heisman Trophy candidate until blowing out his right knee during a close game against Alabama. A few weeks after the season, he was arrested in Knoxville on charges of distributing cocaine, critically damaging his prospects in the NFL. He went undrafted in the 1986 NFL Draft.