Parrish accepted an athletic scholarship to attend the University of Florida in Gainesville, and played halfback and defensive back for coach Bob Woodruff's Florida Gators football team in 1956 and 1957. Memorably, Parrish was named Associated Press "Back of the Week" for his performance in the Gators' 14–7 win over the Vanderbilt Commodores, including rushing for 111 yards, scoring both touchdowns, kicking both extra points, catching an interception, and making seven tackles—including one to prevent the Commodores' tying score.
Parrish received a sports scholarship to attend the University of Florida in Gainesville, and played halfback and defensive back for coach Bob Woodruff's Florida Gators football team in 1956 and 1957. Notably, Parrish was recognized as Associated Press "Back of the Week" for his outstanding performance in the Gators' 14–7 victory over the Vanderbilt Commodores, which included rushing for 111 yards, scoring both touchdowns, kicking both extra points, catching an interception, and making seven tackles—including one to prevent the Commodores' tying score.