If you rent it out you become subject to US tax, have a read of this:
http://www.cra-arc.gc.ca/E/pub/tg/p151/README.html
Or non-resident withholding at 30% if for some bizarre reason you decide not to elect to have it connected to a US trade or business. You can claim a foreign tax credit in Canada so it's basically just a heap of paperwork, you end up paying the same amount.
I'm not sure yet how this will be affected by the new tax treaty, a rental property is a "fixed base" for the purposes of the old treaty but I'm not sure if it's a "permanent establishment" for the purposes of the new one, but regardless, it's US-source income, so there will be US
taxes to pay, just the forms might change a bit so you don't have the election anymore (i.e. it's always treated as income tax).
Anyway the point of my telling you all this is that when you file your 1040NR return you can file a W-7 which will give you an ITIN, which you can use in place of a social security number.
Steve.