The short answer is “it depends, but probably not.” If you’re using your vehicle for personal purposes then you cannot get a deduction on your income taxes for your car insurance payments. But if you’re running a business (i.e. own a business) and use your car primarily for that business, then you should be able to write off at least a fraction of your auto insurance payments.
Though notoriously complicated, the tax form is pretty clear about which line item can be used to right off your car insurance when applicable.
If you were to claim a deduction you would simply add up how much you spent on car expenses for the year -- gas, repair, insurance, depreciation, etc -- and then calculate how much of your car’s usage pertains to your business and deduct that much from your total income. So if you pay $1200 a year in car insurance, and 50% of your car’s usage is for your business you should ask for a $600 deduction.
Obviously you don’t want to mislead the Internal Revenue Service about the nature of your car usage. Businesses for which your car is integral -- generally pertaining to transport and delivery -- are pretty straightforward, and can be defined pretty narrowly by the government. The rest of us will have to continue paying for our car insurance out of pocket.