Not possible. You may not have to be a natural citizen anymore but you at least have to pretend to be!
Unlike with Obama there is no doubt where Arnie was born, Austria. No one is amending the constitution so one 1 jerk can run for President. Only in his dreams!
I would be disposed to support a constitutional amendment that allowed naturalized citizens to be eligible for the presidency if they’ve been U.S. citizens for 35 years (since they would have been U.S. citizens for as long as a 35-year-old natural-born citizen has been a U.S. citizen), but such an amendment would not be in my top 10 list of necessary constitutional amendments. Maybe it could be section 2 to an amendment that clarifies that persons born in the U.S. whose parents are not U.S. citizens or permanent residents shall not be deemed U.S. citizens at birth.
But Arnold Schwarzenegger could never become president even with such a constitutional amendment. The only naturalized citizen whom I can think of off the top of my head whom I would support for president or VP if such amendment was approved would be Congressman Peter Hoekstra of Michigan.
Hahaha!