Yes. The mortgage would need to be a non-recourse type of loan. With a nonrecourse loan, if your IRA fails to make the payments, the only recourse the lender has is the property itself. Also, note that if your IRA obtains a loan, unrelated debt financing income tax (UDFI) will apply, which will subject the portion of the income or gains that are debt financed to Unrelated Business Taxable Income (UBTI).
“Debt-financed property” refers to borrowing money to purchase the real estate (i.e., a leveraged asset that is held to produce income). In such cases, only the income attributable to the financed portion of the property is taxed; gain on the profit from the sale of the leveraged assets is also UDFI (unless the debt is paid off more than 12 months before the property is sold).