Drunk is the correct past participle, but through association with the pejorative connotation of the noun, drank is replacing it more and more in colloquial speech.
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Interesting question. A bit of delving into the Oxford English Dictionary shows that you could at one time or another in our history have said:
I have drank I have drunk I have drunken
as well as I drank and I drunk. I have drank is still current though this dictionary calls it a 'non-standard' form . I have drunken is said to be archaic. Shakespeare used 'have drunk' but the dictionary gives a regular C19 example of 'have drank' too.