Although some argument can be made for Oedipus's own free will and culpability in bringing the prophecies to pass, the play ultimately supports the notion that Oedipus, as well as the other characters, cannot escape the fates that are set.
This determinism is primarily indicated by the failed attempts to stop prophecies from coming to fruition. Indeed, no alternatives are ever given when it comes to the prophecies within the play. When Laius and Jocasta hear the news that their son will wreak havoc on the family and kingdom by murdering his father and marrying his mother, they try to disrupt fate by ordering Oedipus's death. Yet, fate intervenes through the character of the shepherd.
Oedipus, for this portion of his life, is obviously ignorant and helpless and grows up unaware of the prophecy. When Oedipus finally hears the same prophecy, he assumes that it is the only mother and father he has ever known to whom the prophecy refers. So, Oedipus tries to cheat the prophecy by escaping his home and adoptive parents. However, circumstances just happen to lead him back to Thebes, where he meets his father on the road, and they fight, which leads to Laius's death. Then, Oedipus happens to be the only person who is able to decipher the Sphinx's riddle, thereby saving the city of Thebes and winning the hand of the queen, his mother.