He played college football for the Coffeyville Red Ravens before transferring to the Nebraska Cornhuskers, where he won the Heisman Trophy in 1983.

While watching film of Pennsauken's game against nearby Woodrow Wilson High School, one player on the opposing team (Rozier) continually caught Solich's eye.

As the season progressed, Rozier began challenging Roger Craig for the starting position, a job he would eventually win in the fall of 1982 prior to his junior year.

During his junior season, Rozier broke Bobby Reynolds's long-standing school record for rushing yards in a single season, with 1,689 yards, and led Nebraska to a second consecutive outright Big 8 title and a 12–1 record, losing only in controversial fashion to eventual national champion Penn State.

In a performance against Missouri, Rozier came off the bench in the second half to rush for 139 yards on 17 carries to lead Nebraska to a comeback victory despite suffering from a painful hip-pointer injury.

His college career would end in disappointment, losing the 1984 Orange Bowl in which Miami defeated Nebraska 31-30 for the national championship.

Rozier had 138 yards on 21 carries at halftime against a Miami Hurricanes team with the second-ranked defense in football, but he had to leave in the third quarter following an ankle injury.

In 1990, Rozier only played three games for the Oilers, rushing 10 times for a total of 42 yards, before being released after they found no suitable trade partners.

Additionally, a sign was erected in the city proclaiming it the home of the renowned former Nebraska, USFL, and NFL running back.