Most  rental car companies only accept major credit cards, but don't accept debit cards. You may be able to use a debit card, or of course cash, to pay for the car on return, but you will have to have a credit card to pick up the car. Check beforehand on the company web site to verify that you have an acceptable form of payment. 

The name on the credit card you use must be the same as the renter.

If you are using a travel voucher, check any restrictions or additions with the rental company. It may not include taxes or additional fees. Be sure that you know exactly what the voucher will cover. You will be required to present the voucher when you pick up the car.

Very few rental companies accept just a cash deposit. The few that do usually small local operators and they will require a huge deposit.

Some major companies have programs which put you on an internal charge card. Some may pre-approve you for cash rentals, but the process takes time. These need to be worked out and approved well in advance of your need for a car.

Cash rentals have special requirements above and beyond the norm. You should check with each individual company to see how you can qualify.

Advanced approval on file.

A local address with a phone or something permanent in your name.

They may hold your return airline ticket if you are from out of town.

Approval based upon a good credit rating with the credit bureau.

A cash deposit that exceeds the estimated total of the rental bill.

You may be required to purchase their insurance coverage or damage waiver.

Possible limits on the types of car you are allowed to rent.

A minimum or maximum number of days may be required for a cash rental.