Barrett made his major league debut in 1942. He immediately broke into the starting lineup and stayed there until 1946. Regarded as one of the fastest runners in baseball, Barrett led the National League in stolen bases and triples in 1944. In 1946, however, he suffered a knee injury. He was traded to the Braves, and in 1947 he went back to the Pacific Coast League. He retired from baseball in 1951.