American Express cardmembers who have their cards linked to the “Link, Like, Love” app on Facebook may be eligible to get a one-time $25 statement credit after using their card online at costco.com and spending at least $100 in a single transaction by December 31, 2012.

If your card is already linked with Facebook, you can log into your account and check the app to see if the offer is available to you. While it appears to be available on most accounts, it unfortunately doesn’t appear for everyone.

If you do not already have your Amex linked to your Facebook, you can sync your card by visiting https://apps.facebook.com/amexlinklikelove. Once your card is linked, you can load the Amex Sync app. The app will show a number of offers that you can load onto your card. You must register your card first by clicking on the “Add to Card” button for each offer you are interested in, and then make the qualifying purchase with your Amex in order to receive your credit.

Enrollment for the Costco.com offer is limited, so the sooner you can register for the promo, the better. At this time, Facebook appears to be the only social network where Amex has published this offer, so you’re currently unable to register via Twitter or Foursquare.