depends what the points are for. As an example, http//www.nationalcar.com/ItemDetails.do?HelpItemID=DLE lists a few definites, but it might be safer to ask a selection of rental companies.
Not sure how much it varies from state to state, but Mr X just hired a car in Florida and he has 3 points for speeding (tut tut) on his license, no problems arose.
But I agree with Pickle, you may well have to be 25 to hire.
Google some car hire companies and check out their websites.
SOME US hire car companies do, others will charge a hefty surcharge if you are not.
In SOME US states (New York and Michigan) it is in fact illegal for the hire car company to refuse you a car on grounds of age, provided you can get insurance (for which of course you have to pay)