Simple answer: No.
In some states (see link below) the car registration fee includes a personal property (or vehicle valuation) tax . Only that portion of the registration fee is deductible. Even then, it is only deductible as an itemized deduction. That is, you get no deduction if you use the standard deduction. In addition it is subject to the $10K state and local tax (SALT) deduction limit. You can claim the deduction on leased cars, as well as ones you own.
https://www.fool.com/investing/general/2015/05/29/the-states-with-the-lowest-car-tax.aspx
