If you are applying for U.S. citizenship through a process known as naturalization (filing a USCIS form N-400), you can now use a credit card to pay the Form N-400, Application for Naturalization fee.
Most applicants must pay a $680 fee, which includes biometrics fee.
To pay with your credit card, you must file a Form G-1450, Authorization for Credit Card Transaction.
At this time, USCIS accepts payments by credit card ONLY for one application, Form N-400, application for naturalization. This can change in the future. You should always review the form's instructions online before filing.
Here is the form: http://www.uscis.gov/g-1450 and instructions how to pay with a credit card.