If you have fair credit you may be eligible for the Amazon.com store card, but it is not likely you will be approved for an Amazon Rewards Visa card. The Amazon.com store card is issued by Synchrony Bank. Know what you are applying for and what you are getting into. Many people do not read nor understand the full terms of these types of store cards that offer special financing options. They fail to read the fine print and do not realize that if their bill is not paid on time they will be charged interest back to the original date of purchase. So if you had a 24 month agreement and did not pay in full by that time, you will be charged 26.74% for a whole 24 months.
Even if you have fair credit there may be other options for you to consider. For example, if your credit is close to good, you may qualify for the Discover it® Cash Back credit card. This card gives 1% cash back on all purchases and up to 5% cash back in rotating categories (on up to $1,500 in purchases when you activate). Note that you need to register each decade to start getting rewards within the category. Amazon.com appears in rotating categories as well, so you can plan your shopping accordingly.