As per Wikipedia, the paraphrased quotatation is found in Plato's account of Socrates, but it is not confirmed whether Socrates really said such a thing. Is it then okay to say that Plato said 'I know that I do not know'?
Mauro is right.
Xenophon in his Memorabilia (Memories of Socrates) quotes Socrates as saying, with regard to the temple inscription, gnothi seauton, 'know yourself':
That much I made quite sure I knew, at any rate; since if I did not know even myself, what in the world did I know? (https://www.gutenberg.org/files/1177/1177-h/1177-h.htm).
In Plato's dialogue, The Apology of Socrates, mainly a speech rather than a dialogue, Socrates tells us that his friend, Chaerephon:
went to Delphi and boldly asked the oracle to tell him ... whether there was anyone wiser than I was, and the Pythian prophetess answered that there was no man wiser (Apol. 21A; http://classics.mit.edu/Plato/apology.html).
Puzzled by this Socrates finally decided that:
the truth is, O men of Athens, that God only is wise; and in this oracle he means to say that the wisdom of men is little or nothing; he is not speaking of Socrates, he is only using my name as an illustration, as if he said, He, of men, is the wisest, who, like Socrates, knows that his wisdom is in truth worth nothing (Apol.23A-B; http://classics.mit.edu/Plato/apology.html).
Whether Socrates said the things Xenophon and Plato attribute to him, we shall never know. Unfortunately the oracle is not on hand to help but neither asribes to him the view that 'I know that I know nothing'.