Cox was selected by the Red Sox with the seventeenth pick in the first round of the 1973 draft, ahead of Fred Lynn. Listed at 6' 3", 195 lb., Cox played five years in the Boston minor league system, stepping up a class every year, that was hastened by a phenomenal season in 1977 with Triple-A Pawtucket Red Sox. In 95 games, he hit .334 with 14 home runs and 81 RBI, which was highligted by an All-Star selection, helping Pawtucket to clinch the regular season championship. After the season he won both the Topps Minor League Player of the Year and the International LeagueMVP awards, and was recalled by Boston in September 1977.
Cox ended 1977 with a .362 average (21-for-58), and drew considerable attention to himself. Before the 1978 season he was sent by Boston along with Bo Díaz, Mike Paxton, and Rick Wise to the Cleveland Indians in the same transaction that brought Dennis Eckersley and Fred Kendall to the Red Sox. After two years in Cleveland as a backup outfielder and playing all four infield positions, Cox joined the Seattle Mariners in 1980 and the Toronto Blue Jays in 1981, his last major league season.
In a five-season career, Cox was a .245 hitter with 10 home runs and 79 RBI in 272 games.
Currently, Cox works with the Major League Baseball Players Alumni Association in raising money for worthy causes and charities.