Some banks may be offering a VISA Signature card in conjunction with a reward program that works like this, but they are not inextricably intertwined. I have a Citibank Aadvantage VISA card, that earns (natch) AA miles.

The distinguishing feature of Signature is that, while it is generally a standard revolving credit card with a limited credit line, you also can go above the credit limit so long as you pay the excess down on your next regular payment. Sort of like a combined VISA/Amex.

Charlie