Yes, Romney's Mexican-born father was eligible to be president

Romney was born to American citizens living in a Mormon church colony in Chihuahua, Mexico.

Even though he wasn’t born in a United States territory or state, George Romney was given citizenship at birth because he was born to American citizens, essentially granting him the status of a natural-born citizen.

“When you’re born outside the United States to [U.S.] citizens, you have citizenship at birth,” explained Peter J. Spiro, a professor of law and an expert on the law of citizenship at Temple University. “You don’t have to do anything to claim your citizenship. You are a citizen from birth.”

Romney was the first presidential candidate born outside the United States, and his decision to run against Nixon in the Republican primary of 1968 raised many questions.