Swisher's only other big league experience as a leadoff hitter came in 2008 with the White Sox, when Ozzie Guillen wrote his name there 29 times.
With Derek Jeter on the disabled list, the Yankees have a vacancy atop the lineup. Brett Gardner filled the spot on Tuesday, but Girardi made a switch with the Rangers starting left-hander Derek Holland.
Girardi said he based the decision on Swisher's career on-base percentage against lefties (.401), as well as his 2011 on-base percentage facing southpaws (.438).
"I was never a leadoff hitter," Swisher said. "I never had that speed to do it, but I guess my hitting style -- taking a lot of pitches, working walks -- in the situation right now, Skip thought I was the best guy for the job. I'm all for it. I want to win."
Gardner went 3-for-4 with three runs scored and a RBI in New York's 12-4 win over Texas on Wednesday, but said he understood not being in the lineup.
He has hit 38 points lower against lefties (.250) than righties (.288), but his on-base percentage is actually better against lefties (.364) than righties (.361).
"Gardy's been playing exceptionally well," Girardi said. "I'm not married to [the idea that] every time we face a lefty Gardy's not playing, because I like Gardy's at-bats."
Andruw Jones took Gardner's spot in left field, with Swisher in right field and Curtis Granderson in center. Gardner said that despite his good game Tuesday, he didn't arrive at the stadium expecting to be in the lineup.
"I wouldn't say that. I knew we were facing a lefty, so there's really only so many ways you can move things around," Gardner said.