It is best to start with a definition of sophrosyne first. This is an ancient Greek word, which is difficult to translate. It has the following connotations: wisdom, moderation, self-control, and prudence.
Based on this definition, we can say that Oedipus possessed some elements of sophrosyne, but in the end he lacked the more important aspects of it. It is undeniable that Oedipus was wise, but when it came to moderation, he fell seriously short. As a Greek man, he should have known the importance of moderation.
At the oracle at Delphi were the Greek words, "nothing in excess" and "know thyself." These maxims were to remind people that they were not divine. They needed to know their place in the world and not draw too much attention to themselves.
This was something that Oedipus did not heed. He thought he could do anything and everything. For instance, when there was a conflict while he was traveling, he killed his father unwittingly. When there was a plague in Thebes, he thought that he could save the city all by himself.
This pride (hubris) drove the play from the beginning to the end. It also contributed to his blindness. In light of this, we can say that he did not possess sophrosyne in the final analysis.