The analyzing power A~f or p+p elastic scattering at O~, b=8. 64'+0.07' (0, , =18.1') and at a bombarding energy of 183.1+0.4 MeV has been determined to be A~= 0.2122+0.0017. The error includes statistics, systematic uncertainties, and the uncertainty in bombarding energy and angle. This measurement represents a calibration standard for polarized beams in this energy range. The absolute scale for the measurement has been obtained by comparison with p +C elastic scattering at the same energy at an angle where A~i s very nearly unity.