It's never definitively answer either way (which is likely deliberate). I am personally leaning towards the side of no, but there is no hard proof either way. The only evidence we have for the Joker/Arthur being Thomas Wayne's son is that his mother Penny says that he is.
As we come to learn, not only was Penny a Wayne employee, but she claims she and Thomas were lovers and that he is Arthur's father. That's right: Batman and Joker are half-brothers, at least according to Penny.
If there is a Joker sequel, then Batman and the Joker's possible brotherhood might be further explored. However, in the wider DC Universe, the Batman and Joker are not brothers and never were. (Image: Warner Bros.)
In Joker, Thomas Wayne (Batman's father) and Penny Fleck (Joker's mother) are key characters. Penny claims that Thomas is actually Arthur's father.
In the Joker, is Arthur's dad really Thomas Wayne? No, he was adopted, and his mother allowed her boyfriend at the time to abuse him physically and maybe sexually. Arthur found this out when he went to get his medical records/birth certificate from Gotham state hospital.
Penny Fleck was the adoptive mother of Arthur Fleck, a mentally unstable failed comedian who would later call himself the Joker. Much like her son, Penny suffered from an unspecified mental illness.
Jeremiah Valeska is a major antagonist in the television series, Gotham. He is the twin brother of the terrorist cult leader, Jerome Valeska, as well as being the arch-nemesis of Bruce Wayne. Jeremiah is the show's equivalent to the Joker, taking over from Jerome, although both of them never took on the Joker alias.
In Injustice: Gods Among Us, Harley Quinn reveals she gave birth to Joker's daughter, but gave her up for adoption rather than subject her to a life with Joker as a father. Similarly, Harley becomes a mother to twin children in the Batman: White Knight universe, though with happier results.
Major SPOILERS ahead for Joker!
Penny Fleck worked for the Waynes thirty years before the events of the film, with Arthur learning that he was adopted by her while she worked for them.
Harley reveals to Black Canary that she has a four-year-old daughter named Lucy who is being raised by her sister. After discovering she was pregnant, Harley left the Joker for almost a year to have their baby instead of abortion.
Image via Warner Bros. Key to Arthur's spiral is new information he learns from his mother Penny (Frances Conroy), with whom he lives. Arthur finds a letter Penny has written to Thomas Wayne, claiming that Wayne is Arthur's real father.
Frances Conroy, known for her roles in "Six Feet Under" and "American Horror Story," plays the Joker's mother, Penny Fleck, in Joker. How did she get her start?
Seeking the truth in his own roundabout way, Fleck travels to Wayne Manor, where he briefly meets young Bruce Wayne, passing the boy a trick bouquet of flowers through the gate, and finally gets dismissed by Alfred Pennyworth.
Owlman (Thomas Wayne, Jr.) is a fictional character appearing in comic books published by DC Comics. A supervillainous alternate-universe counterpart of Bruce Wayne / Batman, he is depicted as the adult version of Wayne's deceased older brother, who in most iterations dies as a child, before Bruce is born.
In Batman's origin story, Joe Chill is the mugger who murders young Bruce Wayne's parents, Dr. Thomas Wayne and Martha Wayne. The murder traumatizes Bruce, inspiring his vow to avenge their deaths by fighting crime in Gotham City as the vigilante Batman.
He was later repeatedly assaulted by various people and unsuccessfully tried to resurrect his career. Arthur also lost access to his medication and therapist, causing him to succumb to madness as he killed his deceitful mother and took on the identity of the Joker.
A clown and aspiring stand-up comedian named Arthur Fleck lives with his mother, Penny, in crime-ridden Gotham City. Arthur suffers from a neurological disorder that causes him to have random, uncontrollable laughing fits, requiring medication for which he depends on social services.
One of the biggest secrets in the world of DC Comics has been revealed as one of its most iconic characters, an enigmatic villain, gets an official name. In the latest issue of Flashpoint Beyond #5, the Joker's real name has been revealed: Jack Oswald White.
Lucy Quinzel is the daughter of Harley Quinn and the Joker.
As he confronted his mother, Harley's allies found her and informed her that they had found Joker's body. Joker Jr. then revealed himself to be Harley's son who she had abandoned as an infant.
As he confronted his mother, Harley's allies found her and informed her that they had found Joker's body. Joker Jr. then revealed himself to be Harley's son who she had abandoned as an infant.
Yes, I'm referring to the Jokers—and no, that's not a typo. There are three of them.
Barry Quinzel is a minor character who appeared posthumously in the episode "Bensonhurst". He was the son of Nick and Sharon Quinzel and the younger brother of Harley Quinn.