It is very easy, or at least for me it was. I have done it myself in California and am not a US citizen. Opened one last year. Make an appointment or walk-in off the street (Chase, USBank, BoA), have an interview with a banker explaining why you need it, fill out the forms, pay the minimum deposit and some weeks later the card arrives in the mail in Argentina. You can even get a secured US credit card with some banks if the Argentine resident wants a card for spending abroad with.
For those with higher balances or investment products, some private banks in Argentina also will open a US bank account for you remotely and you can get a US amex card remotely too. No need to be a resident, have an ITIN or SSN.
All Argentine residents with US bank accounts need to be aware that the IRS is now sharing account holder details with AFIP automatically from September.