SSN is pretty much required in US unlike SIN in Canada. When I opened my PMA bank account with wellsfargo, they offered me a plat visa without asking for my SSN. But for the mile cards, I think you pretty much need to supply a SSN. If you ever held a work visa of some sort you'd have a SSN but other than that you're out of luck.

Besides, if you haven't established a US credit history, the chances of being approved for those cards is slim to none anyway. Canadian credit doesn't carry over to the US.