The role of free will in Oedipus Rex is especially seen with respect to Oedipus's excessive pride. In fact, we can say that it is his pride that is his tragic flaw, leading to his ill-fated end.
We especially see Oedipus's excessive pride and his use of free will in his account of what happened at the crossroads heading towards Delphi. According to Oedipus, while he was still under the care of Polybus in Corinth, a man proclaimed to Oedipus that Polybus was not his real father. Feeling distraught, he went to the oracle at Delphi to try and learn the truth about his parentage but was only told the horrific prophecy that he would one day kill his own father and sleep with his own mother. He left the oracle in a state of horror struck outrage and anger and came to the place where three roads meet, one heading towards Delphi. There he met with a traveler and his companions who ran him off the road. His pride and his anger led Oedipus to strike out at the driver as well as the man in the chariot, killing the man and all his traveling companions, as we see in Oedipus's lines:
In my anger I struck the driver, turning me off the road, and the old man, when he saw, watched me as I passed the chariot and struck me on the head with the two-pronged goad. But he more than paid for it and soon was struck by the scepter from his very hand ... I killed them all. (834-841)
Oedipus soon learns that the man he killed at the crossroads was his own father, just as the prophecy predicted. Hence, we can see from this passage that Oedipus's actions were not just merely guided by fate. They were guided by his own temper and character traits. Through free will, poor judgement, excessive pride, and lack of control of temper, Oedipus made the choice that day to kill the man who turned out to be his own father. Therefore, we see indeed that free will plays a significant role in the play and a significant role in Oedipus's fate.