Is Oedipus A Political Play?

It is a political play as it is about leadership, power and the conflict between private life and state duties - very important ideas to Sophocles and his fellow Athenians. You might like to have a look at Cliff's Notes, which describe Oedipus the King as a "political thriller." Spark notes have some good background too.

Oedipus is primarily a play about man Vs fate, man running away from his destiny but ultimately falling a prey to what has been destined for him. Nonetheless, the play certainly has political themes involved in it. But you cannot confine this play only to the political scenario. Oedipus, probably in the Second Act, does talk about the power play of politics (please refer to his conversation with Creon). He considers the oracle only a conspiracy against him plotted by Creon and Tiresias. So we can say that it has political streaks in it but is not wholly a political play.