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Wikipedia:

At the time of his birth, Cruz's parents had lived in Calgary for three years and were working in the oil business as owners of a seismic-data processing firm for oil

Breitbart:

The Cruz campaign offered the following statement exclusively to Breitbart News, presented in full (original emphasis): Eleanor was never a citizen of Canada, and she could not have been under the facts or the law. In short, she did not live in Canada long enough to be a Canadian citizen by the time Cruz was born in 1970: Canadian law required 5 years of permanent residence, and she moved to Canada in December 1967—only 3 years before Senator Cruz’s birth. Nothing in the document you sent shows anything to the contrary.

There is no doubt that this is all a little confusing.

http://conservativeamerica-online.com/cruzs-father-rafael-was-previous-married-before-meeting-cruzs-mother-2-of-5/

Following his divorce from his first wife, Rafael Cruz moved to New Orleans, Louisiana for a new job in the Energy Industry. It was while working in New Orleans that Senator Cruz’s parents would meet. His mother, Eleanor Elizabeth Darragh Wilson, was originally from Delaware. Senator Cruz’s mother had come South to study Mathematics at Rice University in Houston, Texas. As she likes to tell it, she refused to learn to type so that when asked about her typing skills, she would say she couldn’t and they would have to hire her as a Computer Programmer instead. It was while working as a Computer Programmer in the Oil Industry, that she met Rafael Cruz.
After their marriage, Senator Cruz’s parents took their careers to the Oil Industry in Canada. It was in Canada that Senator Cruz was born. He was born in Calgary, Alberta, Canada on December 22, 1970.

I think I've documented why I said they were married in New Orleans in 1969. That said, on closer reading that is never really proved by anyplace that I can find, and it's very possible they were not married when Cruz was conceived or born. The birth certificate does say that Eleanor Darragh Wilson was the mother and Rafael Cruz Senior was the father.

That was not her maiden name but her name by a previous marriage, so probably the current legal name as of the birth?

So who exactly is Ted Cruz’s mother, and how did she end up living in Canada? The Texas senator’s mother, Eleanor Darragh, was born to a Irish-Italian family in Delaware and was the first in her family to attend college, the National Journal reported in June. She worked as a computer programmer in New Orleans and Texas, and married Rafael Bienvenido Cruz, a mathematics graduate, in 1969, according to a big story published Wednesday in Maclean’s, one of Canada’s top magazines. Cruz’s parents moved to Canada to process seismic exploration data for oil companies in Calgary, and he was born there in 1970. http://www.ibtimes.com/why-did-ted-cruzs-mother-move-canada-texas-senator-says-eleanor-darragh-makes-him-2266436