Yes, a portion of the registration fee must be charged based on the vehicle's value—as opposed to its size, age or other characteristics.
If part of your registration is indeed deductible, you must itemize your deductions to claim it, rather than using the standard deduction
See https://turbotax.intuit.com/tax-tips/tax-deductions-and-credits/is-your-car-registration-deductible/...
