Can I get an ESTA without a visa card or mastercard?

I've booked to go to the US in two months time and hadn't realised the VWP had in effect been replaced by the ESTA, however I don't have a Visa Card or Mastercard (only a Maestro, that's the only type of card my bank issues). Is there any other way I can get an ESTA? Maybe through the pport office or a travel agent or is it ok to pay for it using someone else's card?