The 27-year-old Bridwell went 1-0 with a 17.55 ERA in five games with the Angels last season. He was 1-1 with an 8.68 ERA in six starts at Triple-A Salt Lake. He missed four months over two stints with an inflamed right elbow.
Bridwell was claimed off waivers by the Yankees in November before returning to the Angels on another claim a month later. He was then designated for assignment last week before being claimed by the A's on Tuesday.
Bridwell is 11-3 with a 4.60 ERA in 28 appearances, including 21 starts, in three seasons in the majors.