Like many internet sites, Ancestry.com has a free trial available. While the trial period is free, they generally ask for a credit card for verification and to begin billing you if you fail to cancel your account. There is nothing fraudulent about this and many, many, many other sites on the internet -as well as many other brick and mortar businesses - will begin billing after a trial period is expired. Be sure to always read the Signup pages carefully!
If you never gave them your credit card for a free trial then I would call your credit company because this is likely a case of theft. I don't think many large corporations are in the practice of randomly billing unknown credit cards and Ancestry.com seems to be fairly reputable. Someone may have stolen your credit # and billed it for themself!