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Yes. There is a no annual fee credit card offered by Delta - the Delta SkyMiles® Blue American Express Card. However, this card won't allow you to earn MQMs. There are only two credit cards that will allow you to earn medallion qualifying miles: the Delta SkyMiles® Reserve American Express Card and the Delta SkyMiles® Platinum American Express Card. The first card offers 100,000 MQM as a sign-up bonus and 15,000 MQM in a calendar year if you meet certain spending requirements. The second card gives 90,000 MQM as a sign-up bonus and 10,000 MQM in a calendar year if you meet offer requirements.

Both cards have high annual fees because they are loaded with Delta and American Express travel benefits and perks. The first card will cost you $450 a year and the second has a $195 annual fee. However, if the high annual fee scares you, you may try credit cards with no annual fee whatsoever, such as the Discover it® Miles card. This card will also let you earn miles you can use on Delta at a rate of 1.5x miles per dollar and they are matched at the end of the first year for new cardmembers.