More and more services offer options to buy bitcoins using your credit card. It is not common practice, since it is not a very secure way of bitcoin exchange and the sellers take some risk when they offer this alternative to customers.
You can buy bitcoin with credit card, but it costs you money and it takes effort. You have to verify your identity before companies allow you to buy bitcoin with a credit card.
Cex.io, a bitcoin trading and mining site, gives you an option to buy digital currencies with your credit card or debit card. The site supports Visa and MasterCard. Again, you must undergo an elaborate and complicated verification process. You also have to wait. If you want to buy bitcoin frequently, Cex.io is a good option for you. The process takes long, however, once you paid, bitcoins will go on your account right away.
Coinbase, a popular bitcoin wallet, provides a variety of options. You can transfer money from your bank account and buy bitcoin for it. Coinbase also accepts credit cards, but only as a backup payment method, it means that you cannot buy bitcoin right from your credit card. If you have a Visa or MasterCard credit card and a billing address within the United States, they accept your card and you can add it to your Coinbase account. Then you have to link your Coinbase account to a United States or European Union based bank account.
VirWox - If you have a free account on Virtual World Exchange, you can buy Second Life Lindens (SLL) with credit card. After that, you can convert your SLL to bitcoins. You can use PayPal or Skrill to complete the process. It means that you can use any credit card that PayPal or Skrill supports. You will have to pay some transaction fee, about 6 percent. However, you do not have to verify your identity, so it is a fast and convenient alternative.
There are other service providers that let you use your credit card to buy bitcoin: Exmo.Com, Bitcoin.de, CleverCoin, CoinMama and CoinCorner.
When you deal with such services, you can always use PayPal to buy bitcoin with your credit card or debit card.