Barrett attended S. H. Rider High School in Wichita Falls, Texas, where he was a three-sport athlete in football, basketball, and track.

[1] In spring 2011, Barrett joined the school's track & field team, recording a personal-best time of 11.10 seconds in the 100-meter dash at the Iowa Park Relays, winning the event, while also running the second leg in the 4 x 400-meter relay, helping them earn a second-place finish with a time of 3:46.05 minutes.

[7][8] On November 29, during the Ohio State-Michigan matchup, Barrett went down with what was later determined to be a broken ankle early in the fourth quarter.

[9] Barrett was cited in the weeks before the injury as a potential Heisman Trophy contender but ended up finishing fifth in the voting.

His injury prevented him from returning during the 2014 season,[10] but he had a successful surgery and was expected to be available in a limited capacity for spring practice.

[11] Ohio State went on to win their next game against Wisconsin, the 2015 Sugar Bowl against Alabama, and the 2015 CFP National Championship, behind the play of third-string quarterback Cardale Jones.

[18] Barrett was the first three-time captain in the history of the Buckeyes football team,[19][20] preceding Tuf Borland as the second.

[22] Barrett went undrafted in the 2018 NFL draft, and was offered to participate in the Indianapolis Colts and the New Orleans Saints rookie minicamps.

[34] On September 17, 2019, Barrett was signed to the New Orleans Saints practice squad following an injury to starter Drew Brees.

[41] Barrett suffered an injury in late March 2022, and after further medical evaluation it was determined he would miss the entire 2022 season.

[42] On July 23, 2022, Barrett was hired by the Detroit Lions as an offensive assistant under head coach Dan Campbell.

On December 10, 2014, police were called to Barrett's apartment after he allegedly choked his pregnant girlfriend and threw her across the room.