Rapada, a sidearm pitcher who has seen limited action in the majors, will compete for a spot in the bullpen at spring training.
Rapada, 28, appeared in just three games for the Tigers last season and is 3-0 with a 4.94 ERA in 27 1/3 major league innings. He has 21 strikeouts and 18 walks.
"He's had quality success against left-handed hitters, mostly in the minor leagues," said Daniels, who said Rapada switched from a more conventional pitching motion to a sidearm delivery when he was with the Cubs a few years ago. "Like a lot of guys, he scuffled early on in his career in the big leagues. He'll come in and compete for a spot."
Rapada had a 2.20 ERA against left-handed batters with 23 strikeouts and six walks (in 16 1/3 innings) for Triple-A Toledo in 2009. That makes him a candidate for the situational lefty spot in the bullpen.
Rapada goes on the 40-man roster as Willie Eyre comes off of it. Eyre cleared waivers and was outrighted to Triple-A Oklahoma City. He has agreed to stay with the club and will be invited to big league camp in Surprise, Ariz., in February.
Rapada is also affordable, as he's not arbitration-eligible and would make less than $500,000 if he's on the Opening Day roster.
Richard Durrett covers the Rangers for ESPNDallas.com. E-mail firstname.lastname@example.org.