Did both of his parents apply for Canadian citizenship?
Evidently. And at the time, his mother was required by Canadian law to renounce her American citizenship.
Before little Ted was born. Rather interesting!
“Did both of his parents apply for Canadian citizenship?”
We know for a fact that Ted Cruz acquired naturalized Canadian citizenship when he was born in Calgary, Alberta, Canada on 22 December 1970. Under the applicable Canadian law in effect on that date Ted Cruz was eligible to acquire naturalized Canadian citizenship at birth only if one or both of his parents were a Canadian citizen or a Permanent Resident of Canada on the path to acquiring Canadian citizenship. Consequently, it must be inferred that one or both of Ted Cruz’s parents had to be a Canadian citizen or at lest a permanent Resident of Canada on the path to Canadian citizenship. When you read the documents associated with the qualifications for acquiring and retaining status as a Permanent Resident of Canada, the applicant must show an intention to make a commitment to permanently reside in Canada and perhaps to become a naturalized citizen of Canada. Such an application could be rejected if the spouse is obviously not interested in making the same commitment. So, it is reasonable to infer both parents acquired naturalized Canadian citizenship or Eleanor was on the path to acquiring Canadian citizenship and stopped short of doing so while Rafael Cruz did acquire Canadian citizenship.