Currently Bitpanda supports buying Tezos with credit or debit card. Please note that this is only available for EU citizensGo to Bitpanda (Tezos credit card support)
Currently no other exchanges with Tezos support accepts direct payments with credit or debit cards.
At the time Tezos will be on more exchanges, it will be possible to purchase XZT using credit card. Currently the only possibility is to buy Bitcoins or other cryptocurrencies (like Ethereum, Litecoin, Dash, etc.) and to look for exchanges with XTZ support. Use the wheretobuytezos.com search form, select the credit/debit card symbol to find an exchange.
Please note: Currently it is not possible to buy XTZ directly with credit or debit card.
Don't Buy Tezos Until You Watch This Video!
To do it indrectly: You have to convert fiat money (like US Dollar, Euro, Pound, Swiss Franc etc.) into cryptocurrency.
Find the Tutorial here: How to buy Tezos (XTZ) Tutorial