Above answer explains issue using current law situation, but I am interested what exactly was law in 1970 when Ted Cruz was born.
An article in Salon claims (which is possibly invalid claim):
As late as 1961, the Supreme Court ruled that the 1802 Naturalization Act only made a child born abroad a citizen if the father was a citizen.
We know that only mother of Ted Cruz was US citizen; his father was a naturalized Canadian.
"Possible duplicate" answer cites 8 U.S. Code § 1401(g) which says:
A person born outside the geographical limits of the United States and its outlying possessions of parents one of whom is an alien, and the other a citizen of the United States who, prior to the birth of such person, was physically present in the United States or its outlying possessions for a period or periods totaling not less than five years, at least two of which were after attaining the age of fourteen years[.]
My question is, when this current interpretation became law? Was it before 1970 when Cruz was born, or after?
This also suggests that Salon article is wrong (which is entirely possible)?
TL;DR: Salon's article would apply to person born before 1932, not to Cruz.