"I've been a free agent before and it really wasn't all that fun, unless you're a major power hitter or a stud starter. If you're a reliever, it's kind of stressful," Frasor said in a conference call. "So when the Rangers showed interest in bringing me back, I was thrilled."
Frasor, 36, joined the Rangers as a free agent last January and held opposing hitters to a .203 batting average in 2013, 16th best among all American League relievers and third best on the Rangers.
His goal is to duplicate those results in 2014.
"I'd like to have a year like I had last year," Frasor said. "I think I'll have the same role -- sixth inning, maybe seventh inning -- and I think the manager's looking for that guy to come in and right the ship and throw strikes."
Frasor made at least 60 appearances for the sixth time in his career last season, and he ranked in the top five among team leaders in appearances, holds (10) and relief innings (49). Originally selected by Detroit in the 33rd round of the 1999 First-Year Player Draft, Frasor has a 3.67 career ERA in the Majors.
Frasor was traded by the Tigers to the Dodgers in 2002, and he was sent to Toronto in '04 in exchange for Jayson Werth. Frasor first established himself with the Blue Jays and wound up pitching for Toronto until 2011, when he was traded to the White Sox in a deal for Edwin Jackson.
After a few months with the White Sox, Frasor was traded back to the Blue Jays before the 2012 campaign, and he pitched there for a season before signing with the Rangers last January.
Frasor has yet to appear in the postseason during his career, and he said returning to a team that was in a late-season pennant race was appealing.
"It made me want to come back a lot," Frasor said of pitching for a contender. "It was just nice to know at this point with the World Series not even over and one of the best teams in baseball wants me back. I'm thrilled, what can I say?"