Peters was selected by the Detroit Tigers in the 1977 amateur draft. He played in the Tigers' farm system for the Montgomery Rebels in 1977 and for the Evansville Triplets in 1978 and 1979. During the 1979 season, he compiled a.320 batting average,.436 on-base percentage, 17 doubles, 10 triples, and 30 stolen bases in 387 at bats. He helped lead the 1979 Evansville team, managed by Jim Leyland, to the American Association championship. Other future major leaguers on the 1979 Evansville team included Kirk Gibson, Jack Morris, Dan Petry, and Tom Brookens. Peters was called up to the Tigers in early September 1979. He made his major league debut on September 8, 1979, and appeared in 12 games in the final month of the season. He started three games at third base and three games as the team's designated hitter and also appeared in two games at second base. He impressed manager Sparky Anderson both with his poised batting style and his range in the field. In 1980, he took over as the Tigers' starting center fielder when Kirk Gibson was injured in mid-June. He appeared in 133 games for the 1980 Tigers, 92 as the starting center fielder and compiled a.291 batting average and.369 on-base percentage with 19 doubles, seven triples, and 13 stolen bases. Peters returned to the Tigers in 1981 though his playing time was limited to 63 games and only 32 games as the team's starting center fielder. He compiled a.256 batting average. In the spring of 1982, Peters underwent surgery to repair a nerve in his right arm that had slipped out of its normal channel through the elbow. He was released by the Tigers after missing the entire 1982 season.
In 1983, Peters signed with the Oakland As. He appeared in 55 games for the 1983 As, including 42 games as a starter in the outfield. He compiled a.287 batting average and had four stolen bases against nine times in which he was caught stealing. Peters spent part of the 1983 season and all of the 1984 season with the Tacoma Tigers in the Pacific Coast League. He had a final stint in the majors during the 1985 season, appearing in 44 games with the Oakland As, principally as a pinch hitter. He compiled a.184 average with the 1984 As and appeared in his final major league game on June 29, 1986. He continued to play for Tacoma in 1985 and 1986. In five major league seasons, Peters appeared in 307 games and compiled a.277 batting average with two home runs, 34 doubles, 10 triples, 80 RBIs, and 20 stolen bases.
Later years
After retiring as a player, Peters worked briefly as a roving instructor for the Houston Astros. He also served as the manager of the Auburn Astros in 1990, leading the team to a 31-46 record. As of 1995, he was living in Tempe, Arizona, and working for the city's parks and recreation department.
