Article II, Section One: No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.
By this strict definition alone, Arnold could run.
I always thought you had to be a natural born citizen, but this clause does not say that.