I’m buying rental real estate with cash. Can I still deduct property taxes even though I don’t have any mortgage interest to deduct?

Yes. The deductions for mortgage interest and real estate taxes are separate items. Claiming one has no impact on claiming the other. The only limitation on the deduction for property taxes is the application of the passive activity loss (PAL) rules. Depending on your rental income, your adjusted gross income, and income and expenses from other investments, you may not be able to deduct some or all of the property taxes in the current year; unused amounts are carried forward and deducted in future years to the extent allowed by the PAL rules.