There are regular travel rewards credit cards issued by major banks that will allow you to redeem miles with any airline, including with Emirates. You will find miles rewards credit card offers from Discover and Barclaycard. Such cards are not tied to one particular airline. In fact, they are not tied to any airline and miles you will earn are basically cash back rewards redeemable for travel and flights in particular. And since Emirates do not offer airline credit card to the US consumers, a travel rewards credit card can be the best option for you.