Ortega's contract was selected from Triple-A Salt Lake on Wednesday.
Ortega began the year at Double-A Rocket City but advanced to Triple-A Salt Lake in late July. He performed well in nine relief appearances with the Triple-A club and posted a 3.75 ERA and 1.33 WHIP in 12 innings. The 24-year-old will be available to make his major-league debut out of the Angels' bullpen, but he should pitch in low-leverage situations.