He played college football for the Texas Longhorns and was selected in the seventh round of the 2015 NFL draft by the Dallas Cowboys.

[1] Swaim played linebacker and received All-section and All-league honors as a senior, after registering 124 tackles (65 solo), six sacks, an interception, a fumble recovery and two blocked extra points.

Swaim enrolled at Butte College where he was converted to tight end and was a two-year starter, helping the team win back-to-back bowls and the 2012 Nor Cal Conference Championship.

[2] After his sophomore season, Swaim transferred to the University of Texas where he was a two-year starter, being used mostly as a blocking tight end and on special teams.

Swaim had one start against the New England Patriots, when he replaced an injured James Hanna and the Cowboys opened in a three-tight end set.

The season-ending injury to Gavin Escobar gave Swaim a chance to play in the last two games and record one reception for no yards.

[7] Swaim became the backup and blocking tight end after James Hanna missed the season with a knee bone bruise.

He started in the ninth game against the Pittsburgh Steelers as the second tight end but suffered a pectoral injury and was replaced by Gavin Escobar.

[10] Swaim entered the season as the Cowboys starting tight end after the sudden retirements of Jason Witten and Hanna.

[21] On August 19, 2020, Swaim was signed by the Tennessee Titans to compete for the blocking tight end role with MyCole Pruitt.

[25] With the departure of Jonnu Smith in free agency, Swaim was named the starting tight end to begin the season.

During a Week 8 34–31 overtime road victory over the Indianapolis Colts, Swaim recorded five receptions for 23 yards and his first touchdown of the season.

[40] He played in 8 games, making one catch for 7 yards and recorded a tackle, but missed several weeks at the end of the season with a concussion.