There are several reasons why you might choose to sign up for a Delta Air Lines cobranded credit card. The airline offers a complete line of credit cards through banking partner American Express, which range from one with no annual fee and limited benefits to a card that costs hundreds of dollars but comes along with premium perks like upgrades and lounge access. However, one of the other most important reasons for seeking out a Delta Air Lines cobranded credit card is if you are looking to earn elite status.