Try getting an ITIN. I got one years ago and I've never lived in the US. I subsequently used it to successfully open a US bank account, as it's the same format as a SSN and it recognised by many financial institutions as if it were a SSN. In my case, I presented my ITIN card so the bank was aware it was an ITIN and not a SSN, but for credit card applications it will probably just be a case of putting your ITIN number on the application form where it asks for a SSN.

http://www.irs.gov/individuals/artic...=96287,00.html