The Angels made the moves Friday before opening a series in Seattle.
Los Angeles acquired the 25-year-old Rasmus from Atlanta last month in a trade for reliever Scott Downs. Rasmus made his major league debut earlier this season, pitching in three games for the Braves.
Rasmus will be the 25th pitcher used this season by the Angels, who have lost four straight to fall to 55-71. They're 18½ games behind AL West leader Texas.
Rasmus is the younger brother of Toronto outfielder Colby Rasmus.