Batwoman season 1, episode 2, "The Rabbit Hole," confirmed that Wonder Woman exists in the Arrowverse. This fully establishes the fate of the full DC Comics' trinity in the shared reality of CW superhero shows, after the 2018 crossover event Elseworlds confirmed that Batman exists on Earth 1 and that Superman doesn't.
The pilot episode of Batwoman saw Kate Kane returning to Gotham City after several years of training abroad, having learned that her first love, Sophie Moore, had been abducted by the supervillain Alice and her Wonderland Gang. After going to Wayne Enterprises in the hope she could use the surveillance equipment there to find some sign of Sophie, Kate discovered the secret entrance to the Batcave and that her cousin, Bruce Wayne, was Batman. This prompted Kate to don the Batman costume in a heroic effort to save Sophie, which ended with the two former lovers almost kissing and Sophie seemingly recognizing Kate despite her all-concealing cowl.
"The Rabbit Hole" saw Sophie confronting Kate directly regarding her close encounter with Gotham City's new "Batman." Sophie asked Kate point-blank if she had been responsible for saving her life several nights earlier. Kate scoffed at the question, denying that it was her and adding "if I were going to save you in a dramatic fashion, I would totally dress as Wonder Woman." This marks the first time that Wonder Woman's existence has been confirmed on Earth 1, but it is not the first time the mythology of the Wonder Woman comics has been utilized by the Arrowverse.
Legends of Tomorrow confirmed the existence of the Amazons and their homeland Themyscira in the season 3 episode, "Helen Hunt." The action of the episode saw the time-traveling heroes journey to the Golden Age of Hollywood, where a time-displaced Helen of Troy had inspired an all-out gang war between the various interests that ran the studios. Helen lamented her fate to a sympathetic Zari Tomaz, revealing that she had been cursed by the gods to inspire men to fight over her and how she wished that she could be a warrior like Zari and her teammates. Unfortunately, there was no way that could happen in either Greece or Troy in Helen's time.
After determining that the historical record said nothing about Helen's final fate once the Battle of Troy was over, Zari tried to find a loophole that would let the Legends take Helen somewhere besides Greece or Troy. Somewhere Helen wouldn't have to live in fear of her curse and could build whatever kind of life she wished for herself. The episode concluded with Zari dropping Helen off on the shores of a beautiful island and the episode's time and location ticker revealing the island to be Themyscira in the year 1253 B.C.
It is unlikely that we will see the Earth 1 version of Wonder Woman making an appearance on Batwoman anytime soon or that she will be played by Gal Gadot. Warner Bros. has been incredibly strict so far about allowing any interaction between their live-action television and film properties. Hopes are high, however, that Lynda Carter might appear as Wonder Woman in Crisis on Infinite Earths, though it is unlikely she'll be the Wonder Woman of Earth 1 if she does.