He accepted a football scholarship from the University of Texas, where he became a three-year starter and a tri-captain. He earned All-SWC honors in 1962 and 1963. As a senior, he helped Texas win its first National Championship. He was named All-American, was the school's first Outland Trophy winner and he finished fifth in the Heisman Trophy balloting. He was also a member of the Texas Cowboys.
In the 1964 Cotton Bowl, he tallied 12 tackles, 2 unofficial sacks of quarterbackRoger Staubach and stopped a scoring threat on fourth down with less than 10 minutes left on the game. He also contributed to the defense setting 2 records by holding Navy without a rushing first down and limiting them to minus 14 yards rushing. The 28-6 win cemented the school's first National Championship.
In 1986, he was inducted into the University of Texas Athletics Hall of Honor. In 2001, he was inducted into the Southwestern Cotton Bowl Hall of Fame.
Although the Steelers thought that Appleton would sign with them, he ended up joining the Houston Oilers of the AFL, who had also drafted him in the first round. The voice of the Steelers, Myron Cope, described the shenanigans both teams used in the attempt to sign Appleton as the "Buddy Dial for Nothing" trade and was one of his favorite stories.
After his career in football ended, he became a manager of a Dairy Queen in Westfield, Texas (20 miles north of Houston) and worked at fast food restaurants, still battling alcoholism and participating in various rehab programs. He eventually ended up at the Fourth Street Inn, a project of the First Baptist Church and Rev. Jimmy Allen, in San Antonio, Texas, where they would feed the homeless and conduct Bible readings. Appleton quit drinking and began studying to become an ordained minister. After working at the Fourth Street Inn, he started his own ministry and spoke across the U.S. talking about his alcoholism and recovery.
Suffering from heart disease, Appleton at first declined a heart transplant operation, but later was placed on the list for a donor heart. However, he died of heart failure in 1992 at age 50.