The White Sox selected Smith's contract from Triple-A Charlotte on Saturday.
The White Sox have exhausted their bullpen depth across their last two games, so they'll bring up Smith and Tanner McDougal to inject their staff with some fresh arms. Smith missed about a month of action after suffering a shoulder injury in June but has given up just one run in 6.1 innings since returning. He'll presumably take on a middle-relief role to begin his big-league career but projects as a starter in the long term.