Can I deduct the purchase of a vehicle as a result of a relocation for work?

NO

No, that is a personal expense, not deductible on a tax return.

While you cannot deduct the purchase price of the car, you may be able to deduct the sales tax you paid for it and a portion of the registration fees. To deduct them, you must itemize deductions on your tax return rather than taking the standard deduction and you must deduct sales taxes rather than state income tax if your state has a state income tax. The only part of the registration fee that could be deducted would be the portion, if any, of the fee that was based on the value of the car. 

See this TurboTax help:

https://turbotax.intuit.com/tax-tips/tax-deductions-and-credits/is-your-car-registration-deductible/L06ja6RwR#:~:text=Annual%20car%20registration%20fees%20may,be%20claimed%20as%20a%20deduction.

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-credits-deductions/define-major-purchase-major-item-sales-tax/L95I4dBi1_US_en_US#:~:text=A%20motorized%20vehicle%20(car%2C%20truck,it%20doesn't%20apply).