Smith hit .293 with two home runs and nine RBI in 47 games with Toronto over the past two seasons.
The 26-year-old is the son of former major leaguer Dwight Smith Sr., who played for the Orioles in 1994.
To make room for Smith on the 40-man roster, Baltimore designated 30-year-old left-hander Josh Osich for assignment on Friday.
Baltimore acquired Osich off waivers from the San Francisco Giants on Feb. 19. Osich is 6-5 with a 5.01 ERA in 160 games with the Giants over the last four seasons.