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You can apply for any travel rewards credit card that has a 0% introductory period. There are a lot of cards that come with 0% intro APR and good rewards on travel purchases. But note that once the introductory period is over, a go-to APR will apply to existing and new balances. Your ongoing interest rate will depend on your creditworthiness. Anyway, we wouldn't recommend carrying a balance on a rewards credit card, especially on a travel rewards credit card because interest will eat all rewards you've earned.
As for the American Airlines credit card, you may like the Citi® / AAdvantage® Platinum Select® World Elite™ Mastercard®, which is similar to the Aviator card. The card's regular interest rate is between 15.99% and 24.99% but, again, you can avoid interest payments if you pay off the card balance in full before the due date each month.