I'm looking for a travel rewards credit cards and wanted to apply for a Gold Delta credit card but Delta cards have high annual fee. Can you recommend me a credit card without annual fee to earn miles towards Delta free tickets?

That's true, airline cards have high annual fees, and Delta Gold, for example, requires you to pay $95 annually, which is more than you should even consider for a travel credit card. There are better options with lesser annual fees or no at all. You can apply for a regular travel rewards credit card. Many of such cards do not have an annual fee or the fee is waived for the first year. All in all, travel rewards cards come with sign-up bonuses and with a rewards program. They allow earning miles or points on travel and everyday purchases. Moreover, if you do not fly often, you can still easily earn miles for a reward airline ticket by simply shopping at your favorite places. Miles earned with travel rewards cards do not expire and can be redeemed for free tickets with Delta Air Lines and any other airline. Also, miles can be redeemed for hotel stays, rental cars or cash.