After attending Wichita Falls High School where he was a first-team all-state selection, Harris played four years of college football for the Texas Longhorns.

[4] A two-way player, he won a starting role at center as a freshman in 1945 and was a consensus first-team All-Southwest Conference (SWC) selection and an honorable mention All-American.

[7][8] The Associated Press (AP), in selecting him All-SWC, noted that the "tall freshman ... never turned in a mediocre performance.

[10] Harris repeated as a consensus first-team All-SWC selection in 1946 while helping Texas go 8–2 with a national ranking of 15th at the end of the year.

[15][16] As a senior in 1948, Harris returned to center, was named co-team captain with Tom Landry, his close friend, and helped the Longhorns compile a record of 7–3–1 with a victory in the 1949 Orange Bowl.

"[19] He won his fourth-straight consensus first-team All-SWC selection, something only one other Longhorn ever accomplished (Bobby Layne), and was selected a second-team All-American by AP, the fourth time in his collegiate career he was named an All-American (either as an honorable mention, third-team, second-team or first-team choice).

[7][20] Harris was named the SWC Defensive MVP by the Houston Post for the 1948 season and was invited to the 1949 Chicago College All-Star Game.