There is evidence to support claims in either direction. Oedipus is most accurately seen as a person balanced between the poles of passion and reason. Circumstances certainly tip the scales toward passion in the end, but even there Oedipus' actions are not without some rationality.
To argue that Oedipus is not rational (and is instead governed by passion), we might look at 1) his stubborn insistence on learning the truth about his own past and 2) the fact that he gouges out his own eyes.
Oedipus is warned that pressing Teiresias will lead to a terrible revelation. He also should have recognized that whatever he learned would not benefit him - how could it? He already has the things he wants and needs. Learning more about his own history can only bring pain. It does. Oedipus is warned repeatedly this will be the case, but his stubborn and perhaps misguided dedication to truth, boldness and courage lead him to a very dark place.
Oedipus' anger and passion is revealed exactly when he would be best served by patience.
When Teiresias refuses to answer Oedipus's call and later resists revealing the king's dark truth, Oedipus grows impatient, hostile, and abusive.
Teiresias delivers the fatal news to Oedipus after the last tirade.
Yet through all this action, Oedipus has systematically approached the source of the truth. He has tracked down the witnesses who are aware of his birth/lineage. He has single-mindedly pursued the solution to the problem he set out to solve - the cause of the plague on Thebes.
It is his intellect that he boasts of most, in fact, in the play. In particular he taunts Teiresias with his most famous accomplishment, solving the riddle of the Sphinx.
I stopped her,
working from intellect, not learning from birds.
In the end, the answer to this question will come down to your own definition of what it means to be a rational person. Oedipus is rational much of the time, but not all of the time. He is rational and intelligent enough to solve the riddle of the plague on Thebes but not restrained enough to control his passions.