The Angels made the moves before Saturday night's game at Texas.
Morin had been put on the 15-day DL on Aug. 4 because of a cut on his left foot. That move was retroactive to Aug. 1.
Morin began this season at Double-A Arkansas and advanced to Salt Lake before making his major league debut April 30. In 32 games for the Angels, Morin is 3-3 with a 2.36 ERA in 42 innings.
The Angels acquired Pestano in a trade with Cleveland on Aug. 7. His only game for them was Aug. 10, when he struck out three Red Sox in one inning.
Before that, Pestano was 0-1 with a 5.00 ERA for the Indians.