Cumpton was recalled from Triple-A Buffalo on Tuesday.
Cumpton signed a minor-league contract with the Blue Jays in early July after a stint with the Southern Maryland Blue Crabs of the independent Atlantic league, and has since posted a 5.63 ERA over six appearances (three starts) at Triple-A. The 29-year-old could make a start for the Blue Jay on Thursday if he isn't needed out of the bullpen in the meantime, Shi Davidi of Sportsnet.ca reports.