You cannot rent a vehicle without a valid driver's license. No, you cannot rent a car without a license. Anyone with a suspended license cannot legally drive, and Budget requires that all tenants have a valid, active license. People with expired and revoked licenses are also not allowed to rent cars.
Keep in mind that rental companies will also refuse to rent a car to you if you have a history of driving under the influence of alcohol, if you are under the state's age to drive rental vehicles, or if you only have a learner's permit. Every case is different, and the car rental counter manager can also make a big difference when it comes to renting a car or not.