Smith played college football for Bo Schembechler's Michigan Wolverines footballteams from 1980 to 1983. As a sophomore, Smith started all 12 games for the 1981 Wolverines and led the team to a record of 8-3 in the regular season and a win over UCLA in the 1981 Bluebonnet Bowl. He had his best statistical season in 1981, completing 97 of 210 passes for 1,661 yards and 15 touchdowns while also rushing for 674 yards and 12 touchdowns. As a junior, Smith again started all 12 games at quarterback for the 1982 Wolverines, leading the team to a record of 8-3 in the regular season, and a berth in the 1983 Rose Bowl, where the Wolverines lost to UCLA, 24-14. Receiver Anthony Carter was Smith's main target in 1981 and 1982, earning All-American honors both years. Smith completed 118 of 227 passes in 1982 for 1,735 yards, though his rushing total dropped to 387 yards on 83 carries. He also threw a career-high 13 interceptions in 1982. He was also selected by the Associated Press as the second-team quarterback on its 1982 All-Big Ten Conference football team. As a senior in 1983, Smith threw four touchdown passes and rushed for a fifth in a 42–10 victory over the Purdue Boilermakers. He led the 1983 Wolverines to a 9-2 record in the regular season and a berth in the 1984 Sugar Bowl, where the Wolverines lost to Auburn, 9-7. Smith completed 106 out of 205 passes for 1,420 yards and rushed for 667 yards on 103 attempts during the 1983 season. Smith was 26-10 as a starter for the Wolverines, completing 324 of 648 passes for 4,860 yards, 42 touchdowns and 32 interceptions. He also rushed 1,736 yards on 329 carries and 31 rushing touchdowns. When he finished his career at Michigan, he was also the team's all-time leading passer, a record that has since been surpassed.
Professional football
In March 1984, Smith signed a contract to play for the Montreal Concordes in the Canadian Football League. During the 1984 CFL season, completing 19 of 45 passes for 263 yards, three touchdowns and seven interceptions. In 1985, Smith was on the roster of the Ottawa Rough Riders. Smith signed a contract with the San Diego Chargers in April 1986, but did not appear in any regular season games with the club.