Where can you sell a cut index card authentic signature from Babe Ruth?

The best place to sell the Babe Ruth cut signature would be through an auction house. If you sell it to a dealer you will only get about half the market value, more or less depending on the condition of the signature. The "authentic" signature would need to be authenticated to get top dollar as well. Signatures that have not been properly authenticated could sell at half the market value or less.

Shop it around with a few auction houses like Heritage Auctions (ha.com) or Robert Edwards Auctions, and see who offers you the most to your needs. They will also help you get the signature authenticated.