No, he’s a senator from Texas. He was born in Canada to an American mother. Which made him American at birth.
Prior to the 1934 Naturalization Act a women could not confer her citizenship to her child. But it gets worst for Cruz. Until the mid late 1800's a women citizenship was determined by her husband. So in 1790 an American woman that married a Cuban became a Cuban citizen. that is why the 1790s' legislation talks about the father not the mother. Its the father that is conferring citizenship not the mother. So if we are going by original intent had Baby Ted been born in 1790 little Ted was Cuban by blood and Canadian by soil. One more time, going by original intent had Baby Ted would not even be a American citizen.
Now how yall turn that into a natural born American citizen is something just just do not get. The only way one can do that is to claim that the constitution does not say what it plainly says. IE living document.
If congressional legislation makes you citizen you are a naturalize citizen not a natural born citizen. Cruz was make a citizen via the 1934 and follow up legislation.