Jake Odorizzi
Jake Odorizzi's time with the Braves was pretty underwhelming as he posted a 5.24 ERA in 10 starts after the Braves acquired him in a trade for Will Smith (more on him in a bit). The Braves clearly weren't fans of what they saw out of him and quickly shipped him out of town to the Rangers after the season in the deal that brought Kolby Allard back to Atlanta. Shoulder surgery kept him off the field for the entire 2023 season for Texas, but he is still technically in line to get a ring.
Robbie Grossman
Another 2022 Braves alum on the list is outfield Robbie Grossman who slashed .217/306/.370 as a part-time player with Atlanta. While he did have some big hits for the Braves and his switch-hitting gave the team some options late in games, his overall production with Atlanta was decidedly lacking. Grossman would end up catching on with Rangers this year, posted a .734 OPS in 2023, and is very likely to be on Texas' World Series roster.
Taylor Hearn
This is a fun one because Hearn actually started his season with the Rangers in 2023 before the Braves traded for him in late July. His time in Atlanta, however, was exceedingly short as he made just a single terrible appearance out of the bullpen before getting traded away to Kansas City for Nicky Lopez just a few days later. Altogether, Hearn made a total of 13 appearances in the big leagues in 2023 for three different teams, but he would still be in line to call himself a World Series champ if Texas handles their business.
Will Smith
Ah, Will Smith....the human heart attack himself. While his time as the Braves' closer from 2020 to 2022 was often frought with a lot of anxious moments, he performed reasonably well overall especially when you factor in his performance during the Braves' 2021 World Series run. After the aforementioned Odorizzi trade that sent him to Houston, he signed a one year deal with the Rangers for this season and posted a very Will Smith-esque 4.40 ERA in 60 appearances for Texas in 2023. At least he isn't used in high leverage situations anymore.