The United States Constitution requires presidents to be "natural born citizens". The original Constitution doesn't define "natural born citizen", but the 14th Amendment states there are two categories of U.S. citizens: those who are born in the United States and those who are naturalized under Acts of Congress.
Sen. Ted Cruz was not born in the United States so his citizenship
is conferred by Congress under its naturalization authority.
Children born to U.S. citizens outside the United States do not
automatically qualify as U,S, citizens under the
Constitution. They can only qualify if a parent meets
the criteria required by the law. For example, when Cruz was
born one U.S. citizen parent had to have lived in the United
States for 10 years before the birth with at least five of
those years coming after the 14th birthday. t
The criteria can be changed by Congress at any time. For
example, Congress might decide to require that both parents be
citizens or change the residency requirements. The specific
criteria required of Cruz or others aren't important.
The important point is that a person whose citizenship is due to
naturalization law cannot be a "natural born citizen".
Cruz has stated that he never checked to see if he became a Canadian
citizen when he was born in Canada until the Dallas Morning News
said he was a Canadian citizen. I hope that he checked to see
if any required applications for U.S. citizenship registration
have been met. If registration requirements have not
been met, Cruz is not any kind of U.S. citizen.