A fast, strong centerfielder, Alexander was an All-Star in both his minor league seasons, hitting .348 with 28 HR and 102 RBI for Fargo-Moorehead (Northern League) in 1936 and .344 with 29 HR in only 79 games for Springfield (Mid-Atlantic League) in 1937. He played in seven games with the Indians that year, but in December 1937 he mangled his left hand in an oil-drill accident and it was amputated.
Alexander became a scout for Cleveland in 1938 and signed Allie Reynolds and Dale Mitchell for the Indians. He joined the White Sox in 1952 and the Dodgers in 1956. Before he left the Dodgers for Philadelphia in 1970, he signed three-quarters of their 1970s infield: Steve Garvey, Ron Cey, and Bill Russell. He was made chief scout of the Phillies in 1979, and in 1987 followed Dallas Green to the Cubs as special player consultant.