Actually, the 'correct' construction to use would be accusative + infinitive:
Cogito me cogitare ergo cogito me esse.
However, this is wrong because the verb 'cogito' describes the actual act of thinking, and can't be used in the sense 'I think George Michael is a good singer.' One must use the verb 'puto':
Puto me cogitare ergo puto me esse.
Of course the whole thing has less ring to it, and the classical authors probably wouldn't have written it this way, nor would your average plebeian speak it like this. But this one will get you more brownie points among retentives like me.