Any answer about Socrates faces the difficulty that we do not have any texts written by Socrates but only texts written about Socrates.
Texts about Socrates have been written by Plato, by Aristophanes and by Xenophon.
The Socrates from Plato's late dialogues is certainly a fiction of Plato. While the Socrates of the early dialogues - Crito, Phaedo - and in particular the Socrates from Apology probably resembles the historical Socrates.
In the following I base my answer on the Socrates from Apology. Here Socrates tells us about his lifelong attempt to obey to the dictum of the God, i.e. to practice a philosophical life. He means the god Apoll from Delphi. Because the Pythia from the Delphic oracle said, speaking in the name of Apoll: Nobody is wiser than Socrates. And Socrates wants to find out the meaning of this dictum.
From this viewpoint Socrates serves one certain god, the god Apoll. On the other hand Socrates fights against the accusation not to believe in those gods which are venerated in Athens. And these are all of the Olympic gods, at least.
Hence the question whether the historical Socrates was a monotheist or a polytheist has to be left open.