It may sound strange to you, but I've never known how this famous statement goes exactly in English... I've just never needed/encountered it in a language different from Bulgarian. Well, obviously me and Descartes don't have much in common in terms of world view (don't the stones exist providing they don't think?)...
Now I see that there are plenty of documents with the "therefore I am" variant, according to Google, even more than the other... The original is in Latin where "ergo sum" corresponds to "I am" rather than "I exist". But it really doesn't matter. Since it will be used as a tattoo, all depends on user's preference and the surface available...