No. We don't have a mechanism to add new provinces to Canada. The current provinces are defined by the Constitution and the only way to change our Constitution is to re-write the whole thing and get all ten existing provinces to agree to it (we don't have a constitutional amendment process.) The best you could do is to be a new territory; those can be created through a simple majority in Parliament.
This is incorrect, adding new provinces is covered under the 7/50 amendment protocol: a motion must pass in the HoC, Senate, and 7/10 provincial legislatures and those provincial legislatures must represent 50% of the Canadian population.