text: I am not sure you can anymore, unless you are a citizen.  The Patriot Act requires institutions to "know your customer."  I recently signed up online for a GMAC Bank account and also for a bank in Chicago.  It used to be they would open any account.  They have to be able to verify your identity first idependently.  If you have idependently verifiable proof of your identity issued by a state in the United States, you may be able to open an account.