No, it’s the same as the US. He’s a citizen at birth by virtue of being born there, and there’s no requirement to do anything else.
http://meurrensonimmigration.com/canada-and-birthright-citizenship/
“Canadian law contains a similar principle. Ever since Canadian citizenship was first granted on January 1, 1947, an individual has been considered to be a Canadian citizen if he/she was born in Canada. This is provided for by section 3(1)(a) of the Citizenship Act, which states that:
3. (1) Subject to this Act, a person is a citizen if
(a) the person was born in Canada after February 14, 1977;
Granting citizenship on the basis of geographic birthplace is known as citizenship jus soli, or “from the soil”. In countries that have citizenship jus soli, or birthright citizenship, it makes no difference what the citizenship or immigration status of the infant’s parents was at the time of birth is (with the exception of children born to diplomats). For example, if a tourist arrives in Canada on a six-month visa, does not disclose that she is pregnant, and then gives birth in Vancouver six months later, then her child will be Canadian.”
“Cruz is also a Canadian citizen, according to the Canadian law experts the Morning News spoke with. Under the Citizenship Act of 1947, anyone born in Canada is automatically granted citizenship at birth unless their parent was a foreign diplomat. (Cruz’s parents were not.) Or, more simply, as University of Montreal law professor France Houle put it: “If a child was born in the territory, he is Canadian, period.””
Actually, Canadian citizenship law is irrelevant to the discussion -- U.S. citizenship law is controlling. Understand that, quite logically, one country's citizenship laws cannot be secondary to another nation's citizenship laws.
Under U.S. law, Cruz was a U.S. citizen the moment he hit the delivery table. The only circumstance under which the U.S. would recognize Cruz' Canadian citizenship would be if he ever chose to opt for it (which he was eligible to do under Canadian law), renouncing his American citizenship in the process.
Since he never made that choice, Cruz was never anything but a U.S. citizen -- under U.S. citizenship law.