Will TurboTax give me the option to pay tax owed with a credit card?

You can pay through a third-party payment processor. However, there is a convenience fee, which is charged by the payment processor.

If you owe the IRS and you're e-filing, select the option Charge my credit card when asked how you want to pay your federal taxes (this question appears in the File section).

The credit/debit card payment option is only available in TurboTax if you e-file your federal return.

 However, there is a workaround if you're paper-filing your return.

Tip: Instead of paying the convenience fee for debit card payment, consider direct debit, which is free.