Barron was born in Orangeburg, South Carolina. He attended Orangeburg-Wilkinson High School, and was a two-sport star in football and basketball for the Wilkinson Bruins. In football, he was named a high school All-American by both PrepStar and Football News, ranked the No. 3 lineman in the nation by PrepStar, named to the All-South team by the Orlando Sentinel, and selected as Jeff Whittaker's Deep South Recruiting Guide South Carolina Player of the Year.
Barron was the nineteenth pick overall by the St. Louis Rams in the 2005 NFL Draft. On August 14, 2005, Barron signed a five-year, $9.2 million contract with the Rams with escalators that could take the value to over $11 million. The contract featured $5.5 million in guaranteed money, not including the signing bonus of $1 million. He would be a starter for the Rams from his rookie season. During his five years with the Rams, Barron was the most penalized player in the NFL next to tackle Flozell Adams with more than 70 calls against him. In a 35-0 loss to the San Francisco 49ers, Barron's poor play resulted him being benched by the Rams staff. Barron became notorious for his false start and holding penalties. In 2009, Barron led the league with 7 holding penalties.
Barron was traded from the St. Louis Rams to the Dallas Cowboys for linebacker Bobby Carpenter on May 10, 2010. Barron's Cowboy career got off to an inauspicious start. In his first game, the Cowboys appeared to have come back from a 13-7 deficit on a touchdown pass from Tony Romo to Roy Williams on the final play against the Washington Redskins on opening day, September 12, 2010. As time ran out of the game, Barron was flagged for holding Brian Orakpo. Because the penalty was called against the offense, the game was over with the Cowboys losing 13-7.
On August 3, 2011, Barron signed with the New Orleans Saints. On August 18, Barron was put on injured reserve and missed the entire 2011 season. He was released with an injury settlement on October 22.