No. The payments on a loan used to acquire the vehicle are not deductible.
However, you can take a deduction for your local transportation related to the management of your rental property. The following is taken from IRS Pub. 527 Residential Rental
Property:
"Local transportation expenses. You may be able to deduct your ordinary and necessary local transportation expenses if you incur them to collect rental income or to manage, conserve, or maintain your rental property. However, transportation expenses incurred to travel between your home and a rental property generally constitute nondeductible commuting costs unless you use your home as your principal place of business. See IRS Pub. 587 Business Use of
Your Home for information on determining if your home office qualifies as a principal place of business.
Generally, if you use your personal car, pickup truck, or light van for rental activities, you can deduct the expenses using one of two methods: actual expenses or the standard mileage rate. For 2016, the standard mileage rate for business use is 54 cents per mile. For more information, see chapter 4 of IRS Pub. 463 Travel,
Entertainment, Gift, and Car Expenses."
