You don't have to cancel your card. Just contact the company (online or phone or mail) and tell them you do not wish to extend your subscription, and they will stop it and refund any money for the automatically extended subscription. At least that's what legit magazines do. This number is calling me, too.....several times a day....my caller id says, "Pennsylvania". Very irritating.
I finally answered after they called every day for a month. They asked me if I was enjoying my magazine subscription of Home and Garden. I had no subscription for this magazine - ever - but she was wanting to extend it for 3 years at 70% off the subscription price. I suspected it was a scam. I declined. Now I don't know if I would have gotten a magazine from them or not (doubt it) but they would have had my name, address and credit card number had I accepted the offer. For the record, I never pay for a magazine or book subscription with a credit card because they "conveniently" extend your service every year until you cancel the card.