Jones was born in Los Angeles, California. His family moved to North Little Rock, Arkansas in 1945, and Jones was a running back at North Little Rock High School. He attended college at the University of Arkansas where he was a member of the Kappa Sigma fraternity. He was also a co-captain of the 1964 National Championship football team. He was an all-Southwest Conference offensive lineman for Hall of Fame coach Frank Broyles and a teammate of Jimmy Johnson. Other notable teammates were Glen Ray Hines, a consensus All-American offensive tackle, Ken Hatfield, Jim Lindsey, and future Outland Trophy winner Loyd Phillips. Several future head coaches were assistant coaches for Frank Broyles and the Razorbacks during his college career in Fayetteville including Hayden Fry, future head coach at the University of Iowa, Johnny Majors, future head coach at Iowa State University, the University of Pittsburgh and the University of Tennessee, and Barry Switzer, Hall of Fame coach of the University of Oklahoma. Jones is one of a very small number of NFL owners who had a significant level of success as a football player, Jerry Richardson of the Carolina Panthers being another.