Simple answer: No.
But taxes aren't simple. There are two possible deductions, included in the fee; personal property tax and sales tax. Both deductions are itemized deductions. If you usually use the standard deduction, an additional $1300 is unlikely to make your total itemized deductions more than the standard deduction ($12,200 Single $24,400 married)
In some states, including CA, the vehicle registration fee includes a personal property tax, which is deductible on the federal return.
Some states don't have income taxes to deduct, so the IRS allows you to deduct either sales taxes OR state & local income taxes (but not both). For residents of most states, it's usually best to deduct income taxes, except when you have a large purchase subject to sales tax, like you. Instead of keeping track of every little thing you bought, You're allowed to deduct an amount from an IRS table (based on income & number of dependents). You are then allowed to add the sales tax on certain large purchases (cars being one of em) to the table amounts.
