At some locations it might be possible, it depends provider/location...you can see it here:-
Under “important information”. First select the car that you want, under important information choose:- payment. It differs per provider...
For example ADVANTAGE :-
Debit Cards which contain an AMEX / Discover / MasterCard / Visa logo are acceptable at time of rental provided the renter has a confirmed flight from the return location on the scheduled rental return date. Debit Cards will be charged for the estimated rental charges plus a $200 deposit at time of rental. Any unused deposit will be credited to the customer`s account within 3 to 5 business days of the rental return, subject to your bank`s processing guidelines.