You can apply for a miles rewards credit card from a major bank. Most major banks issue credit cards that allow earning miles on all purchases. These cards are not tied to a particular airline but allow redeeming miles with any airline, including Asiana Airlines. In addition to regular rewards, there can be a sign up bonus which is often big enough for a round trip ticket. Miles rewards credit cards may also come without annual fees and without foreign transaction fees. So pay attention to the fees as well when you choose a card.
Disclaimer: This editorial content is not provided or commissioned by the credit card issuer(s). Opinions expressed here are the author's alone, not those of the credit card issuer(s), and have not been reviewed, approved or otherwise endorsed by the credit card issuer(s). Reasonable efforts are made to present accurate information, however all information is presented without warranty. Consult a card's issuing bank for the terms & conditions.
All rates and fees, and other terms and conditions of the products mentioned in this article/post are actual as of the last update date but are subject to change. See the current products' Terms & Conditions on the issuing banks' websites.