Strotman signed a minor-league contract with the Astros on Monday, Chandler Rome of The Athletic reports.
Strotman re-signed with the Giants on a minor-league deal on Nov. 19.
Strotman was designated for assignment by the Giants on Tuesday.
Strotman was claimed off waivers by the Giants on Thursday.
The Rangers claimed Strotman off waivers from the Twins on Monday.
Strotman was designated for assignment by the Twins on Saturday.
Strotman was optioned to Triple-A St. Paul on Wednesday, Aaron Gleeman of The Athletic reports.
Strotman is part of the trade package the Rays are sending to the Twins in exchange for Nelson Cruz, Marc Topkin of the Tampa Bay Times reports.
The Rays optioned Strotman to their minor-league camp Tuesday.
Strotman, who fired a scoreless first inning against Atlanta in his first start of spring Sunday, has a 3.86 ERA across the 2.1 innings covering his first three Grapefruit League appearances.