Barton was born in Waco, Texas, on September 15, 1949. He graduated from Waco High School. He attended Texas A&M University in College Station and received a B.Sc. in industrial engineering in 1972. An M.Sc. in industrial administration from Purdue University followed in 1973. Following college Barton entered private industry until 1981 when he became a White House Fellow and served under Secretary of Energy James B. Edwards. Later, he began consulting for Atlantic Richfield Oil and Gas Co. before being elected to Congress in 1984.

Barton was elected to represent Texas's Sixth Congressional seat in his first attempt, defeating Democratic challenger Dan Kubiak with 56 percent of the vote in a contest to succeed Phil Gramm, who left his seat to run for the United States Senate that year. He received 88 percent of the vote in 2000, 71 percent of the vote in 2002 against Democratic challenger Felix Alvarado, and 66 percent of the vote in 2004 against Democratic challenger Morris Meyer.

In 1993, Barton ran in the special election for the U.S. Senate seat vacated by the resignation of Lloyd Bentsen, who became secretary of the treasury in the Clinton administration. Barton finished third in the contest and missed a runoff slot.