Swanson spent his first year in Toledo University, before transferring to Sam Houston State the next year, immediately earning a starting position.  He was an honourable mention All-Southland Conference selection in his sophomore year, a second-team All-Southland Conference player in his junior year, and a first-team All-Southland Conference player in his senior year, getting 46 tackles, 14 pass breakups, and 4 interceptions.  He ended his college career as the all-time leader in interceptions at Sam Houston State, with 14. 
Swanson declared for the 2013 NFL Draft, but went undrafted. One factor of him being undrafted was that he tore his hamstring two weeks before the NFL Combine. He signed with the Indianapolis Colts in time for the 2013 season, but was placed on the injured reserve and was released in October.
San Francisco 49ers
New England Patriots
Swanson then signed for the New England Patriots and played in the pre-season, recovering a fumble against the New York Giants in the fourth quarter of the final pre-season game. Swanson was released and later re-signed to the practice squad on September 17.  Swanson was a member of the Super Bowl XLIX winning squad as a member of the Patriots.
Swanson was released by the Patriots on September 5, 2015. 
Tampa Bay Buccaneers
On October 20, 2015, Swanson was signed by the Buccaneers to the practice squad. On October 27, 2015, he was released by the Buccaneers.
New York Giants
On November 5, 2015, Swanson was signed by the Giants to the practice squad. On November 16, 2015, he was released by the Giants. 
On November 25, 2015, Swanson was signed by the Dolphins to the practice squad. On February 23, 2016, Swanson was waived by the Dolphins. 
On June 13, 2016, Swanson was signed by the Cowboys.