Jason Marquis, who had to miss time because of his injured daughter, is set to return to the rotation next week. That means either Swarzak or Liam Hendriks is headed out of the rotation soon.
Swarzak will be facing perhaps the American League's best lineup from a season ago, with southpaw Matt Harrison on the mound for the Rangers.
"It's always a competition with all the other guys in the league, not just the guys in this clubhouse," Swarzak said. "We're all pulling for each other in this clubhouse but it's always a competition. There are thousands of Minor League guys who are fighting for my job and guys in our organization in Double-A and Triple-A fighting for my job. So it's going to be fun. "We have some good pitchers in this clubhouse. Liam is a good pitcher as well, and I've said before, and I'll say it again, we need as many good pitchers as we can in the big picture."
If Hendriks wins the No. 5 job, Swarzak could be moved to the big league bullpen because he has prior relief experience. Hendriks, however, would likely be sent to Triple-A if Swarzak were to win -- the Twins want Hendriks to continue starting.
Swarzak gave up one run on four hits and two walks in his first start of the season Sunday, adding in a strikeout. Hendriks, who hasn't pitched yet because of food poisoning, is scheduled to start in the series finale Sunday.
Matt Harrison, who will start for the Rangers on Friday, had a good outing in his first start of 2012 as well, throwing six shutout innings on Sunday with four hits allowed, two walks and three strikeouts. He's been working the inside of the plate more, and it's paid off.
"Once you have some success against some guys in, it shows that you're able to pitch inside," said Harrison, who was the winner in a 5-0 victory over the White Sox. "Whenever that happens you're willing to do it more often. Once you start getting strikes in there, you start to open up the inner half. It's a lot better for you when command both sides of the plate and keep the hitters more uncomfortable."
Rangers: Nathan makes his return
Joe Nathan, the closer who recorded 260 of his 263 career saves in seven seasons with the Twins, returns to Target Field on Friday for the first time. He signed a deal with the Rangers in the offseason, leaving Minnesota with a 24-13 record and 2.16 ERA in 460 games.
Nathan hasn't had the best start with his new team, with two saves and two losses - including one blown save - in four appearances.
Twins: Waldrop's rehab going well
Right-hander Kyle Waldrop, who has a strained ulnar collateral ligament in his throwing elbow, threw from 120 feet on Thursday and is scheduled to do the same on Friday, leading up to a bullpen session Sunday.
No date has been set for his return.
"I feel pretty good," Waldrop said. "We took some time off and did some strengthening exercises around the UCL. We tried to take some time off from using the ligament to let it heal itself. So everything is working as planned so far."
The Rangers and Twins both are in the midst of a stretch where three of four games they play are day games.
The Rangers reached the two-million mark in tickets sold for the season Wednesday.