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The Allegiant World Mastercard is available for online application on the airline's website. You can go to the airline's website to review the credit card terms and conditions and to apply. As for the fees, the card comes with an annual fee and with a foreign transaction fee. The Allegiant credit card is not one of the cheapest credit cards for travelers. You can find a travel credit card without an annual fee and without foreign transaction fees. So, you may want to compare other credit card offers before you apply for the Allegiant credit card.