Cruz should just claim he is a negro from Kenya and he will be home free.
The naturalization act Cruz imagines:
Any child born beyond Sea, whose father or mother or both at the time of the birth of such child may or may not have been a citizen of the United States, shall be considered as a natural born citizen of the United States.
One part 1790 Act, one part 1934 Act, shake and pour over ice. Garnish with maple sugar candy et voila, natural born citizenship!