Left-hander Hyeon-Jong Yang was designated for assignment by Texas to make room on the 40-man roster for Santana.
Santana had been designated for assignment by the Dodgers on Saturday. He had a 6.00 ERA (10 earned runs in 15 innings) in a career-high 16 relief appearances this season. The right-hander made 32 appearances over the past four seasons with Los Angeles.
The Rangers have seven days to trade, release or outright Yang to the minor leagues. Yang went 0-3 with a 5.59 ERA in eight games (four starts) with the Rangers before getting optioned to Triple-A Round Rock this week.
Bautista has been with the Rangers' group in Surprise, Arizona, for extended spring training games, but he has not seen action in an official game since 2019. He has a 3-1 record with a 3.70 ERA (23 ER/56.0 IP) over 32 relief appearances combined in the Dominican Summer League (2018-19) and Arizona League (2019).