The straightforward translation is Solus Deus me judicare potest.
However this example illustrates that we should look at the sense behind the sentence before making a word-for-word translation. Possum, potesse, posui literally means "to be able", in the sense of "have the power to do". Generally this is equivalent to "can" in English, but that doesn't mean "can" is always equivalent to possum.
A sentence like the original poster's is typically uttered when a person is trying to discourage others from judging him. Consequently, the sense of "can" is more like the English "should", "ought", or "may". That argues for a subjunctive:
Solus Deus me judicet.
Or a gerundive:
Ego solo Deo judicandus. (judicanda if you're female)
Again, all of these are technically correct; it is context and understanding which allow us to judge which is best. That, in my opinion, is the key to good Latin translation, rather than ransacking the second half of Trauptman's dictionary and choosing the first word next to the entry for "can".