Nicknamed "The Fast Freight from Mississippi State", he was named to the 1952 and 1953 All–Southeastern Conference teams and the 1953 College Football All-America Team. In 1952, he led all NCAA Division I players in points scored, with 120. Parker's 120 points were an SEC record that stood until 1992, when it was broken by Georgia running back Garrison Hearst. Parker won numerous other honors during his college career including being named the Nashville Banner SEC MVP in 1952 and 53, the Birmingham QB Club MVP in 1953 (an award he shared with teammate Hal Easterwood, who was a lineman), and being named the Atlanta Touchdown Club Back of the Year in 1953.