Get Cruz a cheap Hawaiian B.C. Should be no problem.
There are two types of citizens in the U.S. - natural born citizens and naturalized citizens. All citizens are either one or the other. (Non-citizens are either resident aliens or illegal aliens, but that is another topic).
Cruz did not have to apply to become a U.S. citizen. Under U.S. citizenship laws that were in effect when Cruz was born, he was automatically a U.S. citizen at the time of his birth (because his mother was a U.S. citizen who resided in the U.S. for the requisite number of years prior to his birth). Cruz is therefore a natural born citizen and not a naturalized citizen.