You can earn miles by joining one of the frequent flyer programs offered by Star Alliance member airlines. There are 28 airlines in the alliance, including United Airlines which is a major U.S. airline. You can join any frequent flyer program and start earning miles within the whole alliance. There is no additional Star Alliance card, you will have a membership card issued by the airline you join and this card will be recognized by all members.
We recommend you to consider travel credit cards that are more flexible in earning and redeemding rewards. For example, the Discover it® Miles credit card will bring you unlimited 1.5x miles on every purchase. All the miles you earn will be matched at the end of your first year (provided you are a new cardmember). For example, if you earn 30,000 Miles, you get 60,000 Miles. You can redeem them for any travel expenses – any airline, hotel stay, cruises and more.