Party City does not currently offer a way for you to require your guests to pay for a ticket or an event fee before being able to RSVP to your event. We do offer the feature which allows you to collect donation for from event through your PayPal account. This is found in under the Invitation Options menu.
Services like Brown Paper Tickets allow the collection of funds for ticketing. You can certainly use this service or another ticketing service in combination with Party City. Just post your event ticket from the ticket service in the "Event Information" area of your invitation.