You searched for: “calcardophile
calcardophile, calcardophilist (s) (noun); calcardophiles; calcardophilists (pl)
A collector of visiting cards: Mr. Jackson had a whole assortment of cards of acquaintances and friends with their names, addresses, and phone numbers and was known among her friends to be a calcardophile.

A calcardophilist also saves "business cards" when going to business meetings.