The reliever will take the roster spot of right-hander Gerardo Reyes, who was optioned to Triple-A on Saturday.
Herget, 29, was 0-2 with a 4.38 ERA in 12 relief appearances with the Angels earlier this season and had a 2.25 ERA with one save in 10 appearances at Salt Lake.
In 104 career major league appearances (two starts) with three teams, Herget is 5-6 with a 3.29 ERA. He had nine saves for the Angels last season.
Reyes, 30, made his 2023 debut Saturday and gave up a run in one inning of work against the Seattle Mariners. In 30 relief appearances for the San Diego Padres and Angels, going back to 2019, Reyes is 4-0 with a 7.45 ERA.