Yes, you can technically have someone on Social Security cosign your car loan since Social Security checks are a form of income. However, whether or not a lender will accept your grandmother as a cosigner will depend largely on three things:
If you want your grandmother to cosign your loan, shop around with a few different lenders to get a better idea of the kinds of rates you can get. Try to look at a variety of lenders, but focus on places like credit unions that are more likely to offer you a good rate.