The Oakland Athletics selected him in the 13th round (393rd overall) of the 2009 MLB draft.[2] He played the 2009 season with the AZL Athletics, Vancouver Canadians, and Kane County Cougars. He spent the 2010 season with the Cougars and the Stockton Ports, and would also spend the 2011 season with Stockton. In 2012, he was assigned to the Midland RockHounds, where he would play the 2012, 2013, and 2014 seasons. Despite being named a Texas League All-Star in 2012 and 2013, he did not receive a call-up and was released by the Athletics organization on April 2, 2015.
On November 18, 2015, Smith re–signed with Toronto on a new minor league deal. That season, he earned his third career All-Star appearance, this time in the Eastern League, and made a late–season appearance for the Triple–A Buffalo Bisons. In 42 appearances out of the bullpen for New Hampshire, Smith compiled a 1.50 ERA with 68 strikeouts and 5 saves across 72 innings pitched. He elected free agency following the season on November 7, 2016.[3]
Smith again re–signed with the Blue Jays on a minor league pact on December 12, 2016. Smith split the 2017 season between New Hampshire and Buffalo, accumulating a 3.68 ERA in 39 combined appearances before electing free agency on November 6.[4]
On March 24, 2018, he again re–signed with the Blue Jays organization. After pitching for Buffalo in 2018, he was promoted to the major leagues for the first time on August 27,[5] and debuted that day. He was designated for assignment on September 1.[6] Smith elected free agency following the season on November 2.[7]