Barton made his first run for elected office in 1984, when he entered the Republican primary for Texas's 6th congressional district after three-term incumbent Phil Gramm left his seat to run for the United States Senate that year. He finished first in the five-candidate field with 42%, and very narrowly defeated Max Hoyt in the runoff with 50%. He then defeated Democratic nominee and former State Representative Dan Kubiak 57%–43%. Barton was one of six freshmen Republican U.S. congressmen elected from Texas in 1984, known as the Texas Six Pack.