The lender probably collects 1/12 of the estimated annual property taxes in the form of an escrow payment. If so, you still pay the full property tax, just through the escrow account associated with your mortgage.
Most lenders report property taxes paid through escrow in BOX 10 of the Form 1098.
There is no special credit for property taxes, but you can deduct them on Schedule A if you elect to itemize your deductions rather than take the standard deduction for the year.