In 1978, Righetti pitched for the Tulsa Drillers of the Class AA Texas League. In a July game against the Midland RockHounds, Righetti recorded a league-record 21 strikeouts. Jerry Walker, a scout for the New York Yankees, was present in the stands. Yankees owner George Steinbrenner, while negotiating a trade with Rangers owner Brad Corbett that offseason, specifically waited until late in their negotiations to ask that Righetti be added to the trade. On November 10, 1978, the Yankees acquired Righetti, along with Juan Beníquez, Mike Griffin, Greg Jemison, and Paul Mirabella, while the Rangers acquired Sparky Lyle, Domingo Ramos, Mike Heath, Larry McCall, Dave Rajsich, and cash. The Yankees introduced Righetti as "the next Ron Guidry". Righetti was almost traded to the Minnesota Twins in January 1979; the Twins and Yankees were unable to complete a deal in which Righetti, Chris Chambliss, Juan Beníquez, and Dámaso García would have moved to Minnesota in exchange for Rod Carew.