Thompson, who will wear No. 54, appeared in two games for the Angels this year, allowing four runs on five hits and a walk in 2 1/3 innings. He is 3-4 with a 4.24 ERA in 81 career appearances, all in relief.
To make room for Thompson, the A's optioned right-hander Neil Wagner to Triple-A Sacramento. Wagner was recalled by the A's on Tuesday but did not appear in a game with Oakland. He made three relief appearances with Sacramento and was 1-0 with a save, a 5.06 ERA and .273 opponents batting average.