A native of Portsmouth, Ohio, Rice attended Portsmouth High School where he starred in football, basketball and track as well as baseball. He was contracted as an amateur free agent by the St. Louis Cardinals in 1941. Although Rice received his induction notice into the military in 1943, he was turned down because of a physical disqualification. After playing in the minor leagues for four seasons, he made his major league debut with the Cardinals on May 2 1945 at the age of 22.