The Law from the Homeland Security site:
Citizenship Through Parents | USCIS
Cruz's mother was born and raised in Wilmington, Delaware, in a family of Irish and Italian descent.
Ted Cruz born in Canada in 1970, his Mother is a natural born citizen.
The Law:
One parent is a U.S. citizen at the time of birth and the birthdate is before November 14, 1986 but after October 10, 1952
The parents are married at the time of birth and the U.S. citizen parent was physically present in the U.S. or its territories for a period of at least ten years at some time in his or her life prior to the birth, at least five of which were after his or her 14th birthday.
If the U.S. citizen parent spent time abroad in any of the following three capacities, this can also be counted towards the physical presence requirement:
•Serving honorably in the U.S. Armed Forces;
•Employed with the U.S. Government; or
•
Employed with certain international organizations. Which his Mom worked for in the Canadian Oil Field.
Additionally, time spent abroad by the U.S. citizen parent while the U.S. citizen parent was the unmarried son or daughter and a member of the household of a person who meets any of the three conditions listed above can also be counted.
Ted Cruz is a natural Born Citizen under the law.