Jenkins was drafted by the St. Louis Cardinals in the first round of the 2010 Major League Baseball Draft. He signed with the Cardinals for $1.3 million and forwent attending Baylor. Jenkins made his professional debut in 2010 for the Johnson City Cardinals. He appeared in two games, allowing no runs over three innings pitched with two strikeouts. He returned to Johnson City in 2011 and had a 3.86 earned run average with 55 strikeouts in 11 starts. Jenkins was personally invited to spring training by Cardinals manager Mike Matheny in 2012. He pitched that season for the Quad Cities River Bandits. He started 19 games with a 5.14 ERA and 80 strikeouts, before an injury to his latissimus dorsi muscle ended his season. Jenkins started 2013 with the Peoria Chiefs and was promoted to the Palm Beach Cardinals during the season. His season came to an end in August after having surgery on his shoulder. He finished the year with a 4.70 ERA in 13 starts. Jenkins returned to Palm Beach to start the 2014 season. He didn't pitch his first game until June due to the injury from the previous year. In 13 starts he had a 3.28 ERA and 41 strikeouts in 74 innings. After the regular season, the Cardinals assigned Jenkins to the Arizona Fall League.
Atlanta Braves
On November 17, 2014, the Cardinals traded Jenkins and Shelby Miller to the Atlanta Braves for Jason Heyward and Jordan Walden. Jenkins began the 2015 season with the Mississippi Braves. He played in 16 games and went 5-5 with a 3.00 ERA. He was promoted to the Gwinnett Braves of the Class AAAInternational League on July 9 and made his Triple A debut against the Norfolk Tides. Jenkins remained with Gwinnett for the rest of the year, finishing with a total of 25 starts, and a 3.19 ERA. He was named the Braves' Minor League Pitcher of the Year at the end of the season. Jenkins opened the 2016 season in Gwinnett's starting rotation, where he pitched innings and recorded a 2.97 ERA. In June, he began pitching in relief, a move that was seen to increase the possibility of a promotion to the major leagues. On June 16, 2016, Jenkins was called up to the major leagues for the first time. He made his debut six days later against the Miami Marlins, throwing one scoreless inning in relief to finish the eighth inning. On July 6, Jenkins made his first major league start in place of Julio Teherán. He faced the Philadelphia Phillies, pitching innings, while yielding one earned run. On July 29, 2016, Jenkins recorded his first Major League win against the Philadelphia Phillies giving up one unearned run, four hits, and four walks as well as recording four strikeouts through six innings. On August 20, he was sent down to Gwinnett. Jenkins was recalled on September 17.
On January 3, 2017, Jenkins was claimed by the San Diego Padres. He began the 2017 season with the El Paso Chihuahuas of the Class AAA Pacific Coast League. He was released on July 21 after allowing 71 runs in less than 85 innings in the AAA level.
After MLB
In 2019, Jenkins was playing for The Kekambas, a softball team in Texas. On July 31, he was involved in a brawl on the field which resulted in his suspension from the team for the remainder of the season.
