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 attended Florida State University, where he played for coach Bobby Bowden's Florida State Seminoles football team from 2001 to 2004. He was a first-team All-Atlantic Coast Conference (ACC) selection in 2003 and 2004, and was recognized as a consensus first-team All-American in 2003 and a unanimous first-team All-American in 2004. As a senior in 2004, Barron was also one of three finalists for the Outland Trophy. He graduated from Florida State with a bachelor's degree in social science.
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 with more than 70 calls against him. In a 35-0 loss to the San Francisco 49ers, his poor play resulted him being benched by the Rams staff. Barron became notorious for his false start and holding penalties. In 2009, he led the league with 7 holding penalties.
He was traded to the Dallas Cowboys in exchange for linebacker Bobby Carpenter on May 10, 2010.
Barron's career as a Cowboy got off to an inauspicious beginning. In his first game and start in place of an injured Marc Colombo, 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. 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. Although he was active for 10 additional games, he would not play another down during the season and was not re-signed at the end of the year.
On August 3, 2011, Barron signed with the New Orleans Saints. On August 18, he was put on the injured reserve list. He was waived with an injury settlement on October 22.
On May 15, 2012, he signed as a free agent with the Seattle Seahawks. He was cut on August 26.
On March 26, 2013, Barron signed with the Oakland Raiders. He was released to make room on the roster for Tony Pashos on September 2.