“It all depends on when his father became naturalized. If it happened before Ted’s birth...”
His father is Rafael B. Cruz, a Cuban who naturalized as a U.S. citizen in 2005
Ted Cruz was born in Calgary, Alberta, Canada, December 22, 1970, to a US citizen mother and a Cuban citizen father. He is a natural born citizen of Canada (Canadian Citizenship Act, R.S.C. 1970, c. C-19, s. 5(1,3))
Cruz is a naturalized US citizen (8 U.S.C. § 1401(g))
Then....under the guidelines of the Naturalization Act of 1790 Ted Cruz is not a Natural Born Citizen. This Act stipulated that children of citizens born beyond the borders were classified as "Natural Born". If his father did not naturalize until 2005 then Ted is considered a "Born Citizen" (only) because his mother was a U.S. Citizen.
Ted may hold office in any Constitutional area....except that of "Commander in Chief". He is basically in the same category as Obama.....except Barack's father was never a citizen.