[4] Roth then enrolled at the University of South Carolina, where he played college baseball for the South Carolina Gamecocks baseball team in the Southeastern Conference (SEC) of the National Collegiate Athletic Association's (NCAA) Division I. Roth served as a left-handed specialist in the Gamecocks bullpen and also a reserve first baseman, before his first start at the College World Series in 2010 in the National Semifinal, with the Gamecocks in the repechage, playing in the Palmetto Derby, where the sophomore pitcher pitched a shutout to send the Tigers into the repechage.

[6][7] With only four starts to his name heading into the 2011 season, Roth compiled a 14–3 win–loss record and a 1.06 earned run average (ERA), with 112 strikeouts in 145 innings pitched across 21 games as a junior.

Roth led all starting pitchers in NCAA's Division I in ERA in 2011, finishing second in the nation behind Cody Martin of Gonzaga University.

[11] However, Roth chose almost immediately after the 2011 College World Series to return to school, and headed to Alicante (Spain) for a Study Abroad program as part of his International Business degree requirement, and did not sign with the Indians,[14] opting to return to South Carolina for his senior season.

Roth possesses dual citizenship with Great Britain and the United States due to his mother's English heritage.

[21] Roth made his first major league appearance that evening against the Houston Astros, and pitched two innings of hitless, scoreless relief in the Angels' win.

He made his Rangers debut the next day, as a relief pitcher in a game against the Boston Red Sox.

[28] In 15 games (11 starts) for the Triple-A Sacramento River Cats, he logged a 4-4 record and 4.68 ERA with 42 strikeouts across 67+1⁄3 innings pitched.

On July 9, 2017, Roth signed a minor league contract with the Tampa Bay Rays organization.

He made 10 appearances (9 starts) for the Triple–A Durham Bulls, recording a 5.08 ERA with 37 strikeouts in 44+1⁄3 innings pitched.

[30] In 7 games (5 starts) for the Triple-A Iowa Cubs, he registered a 1-2 record and 3.03 ERA with 23 strikeouts over 29+2⁄3 innings of work.

[34] Roth's father worked as a car salesman, until he quit his job to watch his son pitch in the 2011 College World Series.