Barnes attended the University of Arkansas where he initially hoped to play at the end or linebacker position for the Razorbacks.

He ended up as a starter on the offensive line under head coach Frank Broyles.

He helped lead the 1968 Arkansas Razorbacks football team to a 10–1, a #6 rating in the AP Poll, and a victory over Georgia in the 1969 Sugar Bowl.

Following the victory over favored Georgia in the Sugar Bowl, Barnes said: "I have never been associated with a bunch of boys like this.

Barnes later recalled that his childhood struggle with polio gave him "an incentive to work a little harder.