Smith, from North Augusta, South Carolina, was homeschooled through high school and played high school baseball for a team of home schooled students from the Central Savannah River Area. He then enrolled at Darton State College, where he played college baseball. While in college, Smith volunteered as a groundskeeper for the Augusta GreenJackets, the Class A affiliate of the San Francisco Giants, from 2009 through 2011. Eventually he got set up with a bullpen session with Steve Kline, Augusta's pitching coach at the time, who thought Smith had a projectable frame. He threw for Felipe Alou, a special assistant for the Giants, who attempted to sign Smith. Smith instead opted to transfer to Campbell University to continue his college baseball career.
The Giants selected Smith in the 48th round of the 2011 MLB draft.
The San Diego Padres claimed Smith off of waivers on July 6, and assigned him to the San Antonio Missions of the Class AA Texas League. The Padres promoted Smith to the major leagues on September 7, 2016. He made his major league appearance in the 8th inning of a September 7 home game against the Boston Red Sox, and on his first pitch, Hanley Ramírez hit a home run. He was released on December 13, 2017.