In 1963, he was invited to spring training with the Twins and management hoped that the lefty Oliva would counterbalance their right-handed sluggers Bob Allison and Harmon Killebrew. While there, he became friends with teammate, and fellow Cuban, shortstop Zoilo Versalles, who quickly became convinced that Oliva was "the new Ty Cobb", citing their similarities in hitting ability, speed, and arm strength. However, Oliva failed to make the Twins' major league team and was assigned to the Dallas-Fort Worth Rangers, the club's Class AAA affiliate in the Pacific Coast League. Disappointed, Oliva started the season slow, compiling a .235 average in his first two months. He recovered, however, and finished the minor league season with a .304 batting average with 23 home runs and 74 RBI. This earned him a call up for the final few games of the 1963 major league season. Once again he responded with a sizzling bat, hitting .429 in just 7 at-bats.