Outfielder Dwight Smith Jr. was optioned to triple-A Buffalo to clear a spot on the major-league roster.
The 27-year-old Giles is 0-2 with 12 saves and a 4.99 ERA this season. He was optioned to triple-A Fresno on July 11 after appearing to curse at Astros manager A.J. Hinch when he lifted him from the game.
Toronto is also signing right-handed pitcher Mike Hauschild to add an arm to a beleaguered pitching staff. Hauschild had been with triple-A Fresno this year, pitching to a 4.88 ERA in 19 starts. He appeared in four games with the Texas Rangers in 2017.
Darnell Sweeney has been designated for assignment to clear a spot for Hauschild.