Dickerson committed to Texas A&M before reconsidering and deciding amongst Oklahoma, Southern California, and Southern Methodist University (SMU). His great-great aunt talked him into staying in the state of Texas to attend Southern Methodist University because she liked SMU coach Ron Meyer. Dickerson was the subject of recruiting controversy when he started driving a new Pontiac Trans-Am during his senior year of high school. According to “myth,” Dickerson began driving a new Pontiac Trans-Am automobile about the same time he committed to A&M, and, when he signed with SMU, he suddenly was not driving the Trans-Am because it had been destroyed by a vengeful Aggie”. Ron Meyer famously called the car, the “Trans A&M.” At the time he said his grandmother from Mexico bought it for him. Dickerson still refuses to answer on whether or not he accepted anything to attend SMU, saying, “Even if I did take something, I still wouldn’t tell.”
Initially, Dickerson shared carries with Craig James and Charles Waggoner, all three blue-chip recruits in 1979. Waggoner was hurt returning a kickoff their freshman season, leaving Dickerson and James to lead SMU’s running attack, called the Pony Express. Dickerson gained 4,450 yards on 790 carries to break Earl Campbell’s Southwest Conference record for yards and attempts. His 48 career touchdowns tied Doak Walker’s SMU total for career scoring. In his senior year, despite splitting time with James, Dickerson finished third in the Heisman Trophy voting, behind Herschel Walker and John Elway. He was also a first-team All-American in 1982 and a second-team All-American in 1981.