Yes, the Australian Taxation Office (ATO) permits you to pay by credit card - Mastercard; Visa; and AMEX are all accepted. 

Please use the following link.  http://www.ato.gov.au/Business/Payments-to-ATO/How-to-pay/

Other methods of payment include:

-    Cash;

-    Direct Debit;

-    Bpay; and

-    Cheque.