Not directly. We are a shared hosting provider. The credit card issuers impose security requirements on the acceptance of credit cards that prevent you from accepting or storing credit card information on any shared server unless very specific criteria ("PCI DSS requirement A.1") exist and have been audited. We have not been audited for compliance, as it is our opinion that the criteria can only be met by VPS-type services, which we are not.
Therefore in order to accept credit cards and most other payments, you will need to use a third-party secure checkout service. Examples that are known to work include Stripe, Authorize.Net and PayPal.