If I may ...
No he is not. "Ted Cruz is ineligible to run for President of the United States. He was born in Canada, or parents who were Canadian citizens at the time of his birth. Cruz's mother claims to have been born in Delaware but as of last report, the State of Delaware vital records says, no record of Eleanor Elizabeth Darragh Wilson Cruz exists.
Ted Cruz's supporters try to get around "Natural Born" by claiming it simply means any US citizen, an opinion even echoed at Wikipedia!
But if any US citizen could be President, then the qualifier "Natural Born" would not be needed (and is not present in the Constitutional citizenship requirements for Representatives and Senators). Clearly, to the Founding Fathers, "Natural Born" had a specific and obvious meaning, applied exclusively to the Presidency!
The Founding Fathers did not need to define what "Natural Born" meant inside the Constitution as it had been defined in existing legal theory in works such as "The Law of Nations" by Emerich de Vattel, published in 1758 and relied on heavily by the framers of the Constitution. "Natural Born" was already legally defined when the Constitution was written as "born inside the nation."
The inclusion of the "Natural Born" requirement for the Presidency was proposed at the Constitutional Convention by Chief Justice John Kay, who wrote, "Permit me to hint, whether it would not be wise and seasonable to provide a strong check to the admission of Foreigners into the administration of our national Government and to declare expressly that the Command in Chief of the American army shall not be given to, nor devolve on, any but a natural born Citizen..."
The intention is clear that the Presidency not be open to anyone not born within the United States.
In addition, there are no less than four United States Supreme Court Decisions that reaffirm that "Natural Born" means "Born inside the nation."
The Venus, 12 U.S. 8 Cranch 253 253 (1814)
Shanks v. Dupont, 28 U.S. 3 Pet. 242 242 (1830)
Minor v. Happersett , 88 U.S. 162 (1875)
United States v. Wong Kim Ark, 169 U.S. 649 (1898)
There has never been a United States Supreme Court Decision that ruled "Natural Born" as having any other meaning than "born inside the country."
All of Cruz's supporters, including the corporate media, are demonstrating either an ignorance of the US Constitution, or an utter disregard for it. This tells us that were Cruz to become President, he would continue the long and tragic tradition of recent Presidents to ignore the Constitution to the detriment of the people.
The Constitution is the original contract with America. It is the rules by which We The People allow the government to act as caretaker of our National Sovereignty. If a politician does not wish to work within the restrictions and rules of the Constitution, the honorable thing to do is resign and find useful employment. If Ted Cruz's supporters wish to live in a nation not protected by the Constitution they are free to move elsewhere.
But under the rules this nation operates on, Ted Cruz is not eligible to be President of the United States."