Yes, but not with most insurance companies.
Most insurance companies require that you have an insurable interest in order to be able to insure something such as a car.
Some CarInsurance.com companies require that your name appear on the title or registration in order to be able to purchase an auto policy in your name.
If you get a quote with us, we do have a company that will give you insurance for a car that is not registered in your name (Esurance), but the owner will be required to be listed on the policy. Start your quote above and select Esurance on the quote page.