Right-handed reliever Dustin Nippert and infielder Esteban German, who didn't play in the division series against Tampa Bay, were removed from the roster. Nippert made one appearance against Tampa Bay in the first round, giving up two runs in an inning.
Kirkman, a rookie, had a 1.65 ERA in 14 appearances during the regular season. Rapada had a 4.00 ERA in 13 games.
Texas carried seven relievers during the first-round series. Manager Ron Washington had said the Rangers would add another reliever against the Yankees. Game 1 is Friday night at Rangers Ballpark.