No. An individual’s charitable contributions can be deducted only as an itemized deduction. Even if the rental property is a trade or business, with income and expenses reported on Schedule C rather than on Schedule E, and you can somehow tie the charitable contribution to the business, the donations are still taken by the owner only on Schedule A.
Debt used to buy, build, or construct a principal residence or second home and that generally qualifies for a full interest expense deduction.