The sales tax is not a deductible business expense for a personal vehicle used in business.
If you use the standard mileage method, you can deduct as a business expense, 58.5 or 62.5 cents per mile, depending on the dates. The standard mileage rate includes built-in amounts for all car expenses, including the purchase cost (fuel, repairs, insurance, depreciation). You can't take an extra deduction for specific costs of buying or operating the car.
https://www.irs.gov/tax-professionals/standard-mileage-rates
If you use the actual expense method, one of your expenses is depreciation--in other words, an allowance for wear and tear based on the cost of the vehicle. You include sales tax in the cost when you calculate the allowable depreciation. Very roughly speaking, depreciation on a car is taken over 5 years, so if you used the car 40% for business last year, your depreciation for the first year would be 1/5 the cost x 40%. That's how you recover sales tax for the business use portion, by including it in the cost basis when you calculate depreciation.
If you use the vehicle more than 50% for business, you may have additional options to claim the depreciation faster than over the first 5 years of the vehicle life, but I am not an expert on those methods. See chapter 4 of IRS publication 463.
https://www.irs.gov/forms-pubs/about-publication-463
If you are the sort of person who drives a car for a long time, the standard mileage method will usually result in a larger tax deduction over time. If you are the sort of person who will trade it in in 5 years or less, the actual expense method may result in a larger overall deduction.
