Your residency (address) can affect your eligibility for voting in local elections in a given jurisdiction, but any American citizen can vote for President regardless of how recently he/she might have moved.

That's the law, but of course where there are crooked political hacks in the state attorney general's office, it's quite possible that this law will be broken and selected citizens (the old, the poor, blacks, active duty military, etc.) will be denied the vote.