Santana was traded from the Dodgers to the Rangers on Thursday in exchange for left-hander Kelvin Bautista.
Santana was designated for assignment by the Dodgers on Saturday, and he'll now head to Triple-A Round Rock to begin his time with his new organization. The right-hander made 16 relief appearances for Los Angeles to begin the year and posted a 6.00 ERA and 1.93 WHIP in 15 innings.