Oedipus demonstrates that he accepts responsibility for murdering Laius, his father, and marrying Jocasta, his mother, by blinding himself with pins that he sticks into eyes.
Before the truth was forced on him, Oedipus had too much hubris or pride to even imagine he could be Laius's killer. When Creon arrives back from the oracle with the news that only bringing Laius's murderer to justice will end Thebes's devastating plague, Oedipus first offers leniency and then, when nobody comes forward to confess, angrily decrees a harsh penalty for the murderer, even should he be a member of Oedipus's own family.
To Oedipus's credit, once the truth becomes clear to him, he does not try to evade responsibility for his actions. He could have fallen back on the fact that he did not know he was killing his father or marrying his mother, but he realizes that doesn't matter. He did what he was fated to do and must suffer the consequences, which include his own blindness and exile, as well as Jocasta's suicide.