As there is no SkyTeam credit card, you should choose one that is offered by any of SkyTeam alliance member airline. SkyTeam includes 20 airlines like Delta Airlines, Korean Air and other, you can choose what airlines you prefer the most, compare their credit card terms and apply. Keep in mind that airline co-branded credit cards give good rewards on airlines purchases and often only 1 point or mile for all purchases, so you will need to fly a lot to earn miles. Also there may be some restrictions when redeeming rewards. If you do not want to apply for a credit card of a particular airline, consider travel credit cards that are more flexible in earning and redeemding rewards. You will earn good rewards on all your purchases. Earned miles or points can be used for any airline you want, not for SkyTeam alliance only. What is more, rewards are often may be used for other travel expenses, like cruises, hotel stays, car rentals and more.