Leasure allowed one hit and struck out one across a scoreless inning in Sunday's win over the Cardinals.
Leasure earned a save after he pitched two-thirds of an inning, retiring both batters he faced in Sunday's 4-2 win over the Rays.
Leasure allowed one earned run on two hits across one inning to earn a hold Tuesday against the Twins.
The White Sox selected Leasure's contract from Triple-A Charlotte on Wednesday, Daryl Van Schouwen of the Chicago Sun-Times reports.
Leasure has not allowed an earned run across six innings of Cactus League action.
The Dodgers traded Leasure, Nick Nastrini and Trayce Thompson to the White Sox on Friday in exchange for Lance Lynn and Joe Kelly, Jeff Passan of ESPN.com reports.