The Rangers acquired Silseth and catcher Logan O'Hoppe from the Angels on Wednesday in exchange for infielder Angel Arredondo, Jeff Passan of ESPN.com reports.
Silseth has found success in a relief role for the Angels this season, posting a 2.72 ERA and 48:22 K:BB over 39.2 innings. Though he's unlikely to unseat All-Star Jacob Latz as the Rangers' closer, Silseth should continue to work fairly often in high-leverage situations with his new squad.