The question is did his father naturalize to become a U.S. citizen before Ted was born? If not, he is not a natural born Citizen eligible for Article 2 Section 1.
His father naturalized in 2005 but it doesn't really matter because no court seems willing today to adopt the birther definition of natural born citizen that requires both parents to have been U.S. citizens. This means you are free to vote against him on this basis if you wish, but if you think Senator Cruz is going to face any legal hurdles over his eligibility due to the fact that his father was not a citizen, think again. It's not going to happen. It wasn't an issue when Bill Richardson ran for President. It wasn't an issue when Barack Obama ran for President. And it won't be a legal obstacle for Marco Rubio, Bobby Jindal, Nikki Haley, or anyone else with foreign parentage who decides to throw their hat into the ring.
The courts just aren't buying this.