The Los Angeles Angels of Anaheim selected Cowart in the first round, with the 18th overall selection, in the 2010 Major League Baseball draft. Though he committed to play baseball at Florida State University, Cowart signed with the Angels. Cowart played for the Cedar Rapids Kernels of the Class AMidwest League and Inland Empire 66ers of the Class A-AdvancedCalifornia League in 2012. Between the two levels, he had a.276 batting average and 16 home runs in 135 games. Promoted to the Arkansas Travelers of the Class AATexas League in 2013, Cowart struggled, batting.221 with six home runs and 124 strikeouts in 132 games. Returning to Arkansas in 2014, Cowart batted.223 with six home runs and 99 strikeouts in 126 games. After two poor seasons, the Angels assigned Cowart to Inland Empire to start the 2015 season, where he demonstrated an improvement in plate discipline. In June, due to promotions of C. J. Cron, Efren Navarro, and Kyle Kubitza to the major leagues, the Angels promoted Cowart to the Salt Lake Bees of the Class AAAPacific Coast League, where he batted.323/.395/.491. The Angels promoted Cowart to the major leagues on August 18, 2015. He made his major league debut that night. After the 2015 season, Cowart changed his uniform number from 41 to 22. In 2016, he appeared in 31 games for the Angels, hitting.176. The following season, he played in 50 games, hitting.225 with 3 home runs. He began the 2018 season in AAA, being recalled during the season. In 47 games, he hit.134 with 1 home run and 10 RBIs. On December 10, 2018, the Seattle Mariners claimed Cowart off of waivers and announced he would come to spring training as a third baseman and as a pitcher. The Mariners designated him for assignment on January 21, 2019, and he was claimed off waivers by the Detroit Tigers on January 24. Cowart returned to the Angels on February 23, 2019, when they claimed him off waivers from the Tigers. He split the 2019 minor league season between Mobile and Salt Lake. He hit a combined.276/.331/.433/.764 with 9 home runs and 62 RBI, while going 1-2 with a 10.19 ERA over innings pitched. On September 18, the Angels selected Cowart's contract. Cowart elected free agency following the 2019 season. On December 20, 2019, Cowart signed a minor league contract with the New York Yankees.