Natural born is a requirement in the Constitution that is defined in the Naturalization Act of 1790. It defines it as birth from citizen parents. Cruz’s father was not a citizen.
The Naturalization Act of 1790 was superseded by the Naturalization Act of 1795. So the Naturalization Act of 1790 ceased to be law once the 1795 act was signed into law.
Regardless, the text of the 1790 law states:
“And the children of citizens of the United States that may be born beyond Sea, or out of the limits of the United States, shall be considered as natural born Citizens: Provided, that the right of citizenship shall not descend to persons whose fathers have never been resident in the United States.”
There is an interpretation issue here. Does the plural “citizens” refer to both parents, or does the plural “citizens” refer to the many covered by the law? Given the text says “and the children of” [plural], not “and a child of” [singular], it is probably the many covered by the law.
It is not clear from the text. Mark Levin interprets the 1790 law would confer Natural Born Citizenship status on Cruz if it were still the law today.
What is clear is if a woman traveled overseas and had a child of a foreign man who never was a U.S. citizen or resident, citizenship would not transfer.