The St. Louis Cardinals selected Kelly as a third baseman in the second round and 86th overall selection of the 2012 amateur draft. He signed with the Cardinals, receiving a $1.6 million signing bonus. He began his career with the Johnson City Cardinals of the Rookie-levelAppalachian League. He hit.225 with nine home runs and 25 RBIs in 56 games for Johnson City. In 2013, he was promoted to the Peoria Chiefs of the Class AMidwest League. He struggled with Peoria, and was demoted to the State College Spikes of the Class A-Short SeasonNew York–Penn League. In 113 games between the two clubs he batted.257 with six home runs and 45 RBIs. In 2013, Kelly and Gary LaRocque, the Cardinals' director of player development, discussed his switching positions to catcher. Kelly agreed to the switch, and began to transition during the 2013–14 offseason. He played for Peoria in 2014, and batted.248 with six home runs and 49 RBIs in 98 games. He spent the 2015 season with the Palm Beach Cardinals of the Class A-AdvancedFlorida State League and compiled a.219 batting average with eight home runs and 51 RBIs in 108 games. He won the 2015 minor leaguesRawlings Gold Glove Award for catchers and was ranked the tenth-best prospect in the Cardinals system prior to the 2016 season, per Baseball America. Kelly began the 2016 season with the Springfield Cardinals of the Class AATexas League. He was selected to the 2016 Texas League All-Star Game and to the 2016 All-Star Futures Game. Kelly was promoted to the Memphis Redbirds of the Class AAAPacific Coast League on July 11, 2016. The Cardinals purchased Kelly's contract on September 4, 2016, promoting him to the major leagues. In 96 games between Springfield and Memphis prior to his call up he batted.289/.343/.395 with six home runs and 32 RBIs. He made his major league debut on September 5 at Pittsburgh and, in his first ever at-bat, hit a line-drive double in the eighth inning, and then scored his first run. After the season, the Cardinals assigned Kelly to the Glendale Desert Dogs of the Arizona Fall League. The Cardinals also named Kelly their 2016 Minor League Player of the Year. Kelly returned to Memphis to begin 2017. He was recalled to St. Louis on July 21 and spent the remainder of the season there. In 68 games for Memphis he posted a.283 batting average with ten home runs and 41 RBIs, and in 34 games for St. Louis he batted.174/.240/.217. MLB.com ranked Kelly as St. Louis's third best prospect going into the 2018 season. He began the season with Memphis and received his first 2018 promotion to the major leagues on May 6 when Yadier Molina was placed on the disabled list. However, Kelly was placed on the disabled list on May 17 with a right hamstring sprain.
Arizona Diamondbacks
On December 5, 2018, the Cardinals traded Kelly, Luke Weaver, Andy Young, and a draft pick to the Arizona Diamondbacks in exchange for 1st baseman Paul Goldschmidt. On March 30, 2019, Kelly hit a game-winning RBI in his debut as a Diamondback. On May 4, 2019, he hit his first career home run.
Personal life
Kelly's mother, Traci, and his father, Mike, are from Chicago. The Kelly family spent two years living in Toronto during Carson's youth. His younger brother, Parker, played college baseball for the University of Oregon and was drafted by the Cardinals in the 20th round of the 2018 MLB draft.
