The Costco Anywhere Visa ® Card by Citi is a personal credit card from Costco Anywhere Visa ® Card by Citi. Application typically pulls a hard report from Experian. The annual fee is No Annual Fee with paid Costco Membership. Rewards: Earn cash back at Costco and everywhere else you shop. Cash back: No limits on cash back. Application rules: Recon: (800) 695-5171 Recon Alt (community-reported, unverified): (888) 201-4523.