The deal came while the Rays played at Yankee Stadium on Monday night.
The 29-year-old Bemboom was reinstated from 60-day injured list earlier in the day and designated for assignment. He had been sidelined by a sprained left knee.
Angels starting catcher Jonathan Lucroy is expected to be out for about three weeks after he undergoes surgery Tuesday on the fourth broken nose of his career, according to manager Brad Ausmus.
Bemboom made his major league debut this year and went 2-for-5 in three games. He was among a team-record six catchers used by Tampa Bay this season.
Drafted by the Angels in 2012, he played in their minor league system for five seasons.