Legal Question in Constitutional Law in Texas

Yes. Children of American citizens are American citizens from birth, regardless of where they are born. That's just as true when only one parent is a citizen as when both are. So Cruz is in the clear.

This is an area where the law isn't 100% certain. There is some room to argue that Cruz isn't eligible, but not much. Few lawyers would agree with those arguments. If a court had to decide the matter, it would almost certainly rule in Cruz's favor.