No, you cannot get car insurance just using an international driving permit (IDP).
Most all insurance companies will require that you have a US driver's license in which to rate you on for a personal auto insurance policy. You may be able to start a policy with a foreign license but then you must obtain a US license in a short period of time, normally 30 to 45 days.
There are some specialty insurance providers that may allow international drivers with valid foreign licenses to obtain and maintain auto insurance however we are not aware of any insurance company that will insure you only using an international driver permit.
The IDP is a translation of the information on your foreign driver's license, not a valid driver's license. It is typically your country's valid driver's license that allows you to drive in the US though an IDP may be helpful to an insurer, police, etc since it is a translation of your license in English, it is not a valid license on its own and thus cannot be used to drive a vehicle or get insurance on.