Oedipus Rex, a tragic victim of fate, easily meets the criteria of the tragic hero. According to Aristotle, a tragic hero can not be extremely virtuous or evil, they must be on the middle ground. This is true of Oedipus, in the eye of the public, he is a concerned, caring individual, but he is also capable of atrocities. He does have the blood of his own father on his hands. The fact that he did not know that he was killing his own father places him in the median between virtuous and evil. A tragic hero must also have a frailty, or tragic flaw.
This is also true of Oedipus. The fact that he has murdered his father and fathered children with his mother are sufficiently adequate to qualify him as an individual with a tragic flaw. He also seems to be a rather arrogant individual, another characteristic capable of being a tragic flaw. This can be derived from the way Oedipus speaks. Oedipus also goes through a reversal of fortune, another characteristic of a tragic hero. It look as if he has a solution to the problem Thebes faces, when in fact he is the problem.
This is hidden from him, when he is made aware of this, and the atrocities he has committed, he endures great suffering. His wife and mother commits suicide, and due to the burden this situation puts upon him, he gouges his eyes out. Due to his level of suffering, the audience or reader feels a sense of pity for Oedipus, which is another characteristic of a tragic hero. His flaw causes him to commit an atrocity, the emotional and physical consequences of which destroy him, causing the audience to feel pity for him. Oedipus Rex meets all of the criteria necessary to become a tragic hero, therefor he is.