After graduating from Kentucky in 1949, Phelps was selected by the Cleveland Browns of the National Football League (NFL) in the sixth round of the 1950 draft. The Browns had recently joined the NFL after four years and four championships in the defunct All-America Football Conference. Led by quarterback Otto Graham and fullback Marion Motley, the Browns finished the 1950 season with a 10–2 record and won the NFL championship over the Los Angeles Rams. Phelps was used primarily on kickoffs and punts, registering 499 total return yards and one punt return for a touchdown in 1950. He also had 198 rushing yards and a rushing touchdown.