Rollins spent most of last season at Triple-A Tacoma, where he was 5-0 with a 3.77 ERA and a 0.99 WHIP. Left-handed hitters batted .247 off him, while right-handers hit .226.
Rollins is a native of East Texas who pitched at First Baptist Academy in Carthage and Dallas as well as San Jacinto Junior College. He was a 24th-round Draft pick by the Blue Jays in 2011 and was included in a 10-player trade with the Astros on July 20, 2012.
Rangers pitching coach Doug Brocail worked with Rollins in the Astros' organization.
"He is an aggressive lefty with a history of throwing strikes, a good fastball and feel for a change," Rangers pro scouting director Josh Boyd said. "He earned a lot of respect from Brocail for his competitive demeanor, too."
The Mariners selected Rollins in the 2014 Rule 5 Draft, but he was suspended for 80 games at the beginning of the '15 season when he tested positive for Stanozolol, a performance-enhancing drug.
Rollins is now the fifth left-handed reliever on the Rangers' 40-man roster, along with Jake Diekman, Alex Claudio, Dario Alvarez and Andrew Faulkner.
T.R. Sullivan has covered the Rangers since 1989, and for MLB.com since 2006. Follow him on Twitter @Sullivan_Ranger and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.