I faxed in my application and got approved for a greater than 5k USD credit limit after a few weeks. Took a call to read another disclosure, and a second call to verify info on the TU Canada report.
No SSN, no US credit history to speak of.
Had existing TD Canada borderless and TD Bank US checking account at time of application.
Haven't received the card yet, but it shows up on my TD Bank US online banking.
http://www.tdbank.com/personalcreditcard/aeroplan.html