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Yes. There is a no annual fee credit card offered by Delta - the Blue Delta SkyMiles® credit 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 Reserve® credit card and the Platinum Delta SkyMiles® credit card. The first card offers 1,000 MQM as a sign-up bonus and 15,000 MQM in a calendar year if you meet certain spending requirements. The second card gives 5,000 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.