The trade was announced Tuesday, five days after the Dodgers designated Sborz for assignment while signing free-agent ace Trevor Bauer. The Rangers designated right-hander Jimmy Herget for assignment.
Sborz, 27, made four relief appearances over four stints with the Dodgers in 2020. He allowed one run in 4⅓ innings. Sborz didn't pitch in the postseason for the World Series champions.
In 11 appearances over two seasons with L.A., Sborz allowed nine runs in 13⅓ innings. He was a second-round pick out of Virginia in 2015, when he helped lead the Cavaliers to the College World Series championship as most outstanding player.
The 19-year-old Zambrano's only professional action came with the Rangers' Dominican Summer League affiliates in 2019. The right-hander combined for a 2.55 ERA 12 games, including 11 starts.
Herget had a 3.20 ERA over 20 games with one start for the Rangers in 2020 after being claimed on waivers from Cincinnati. The Rangers have seven days to trade, release, or outright Herget to the minor leagues.