We have obtained a smooth time series for the electric vector position angle (EVPA) of the blazar OJ 287 at centimeter wavelengths, by making ±nπ adjustments to archival values from 1974 to 2016. The data display rotation reversals in which the EVPA rotates counterclockwise for ∼180° and then rotates clockwise by a similar amount. The timescale of the rotations is a few weeks to a year, and the scale for a double rotation, including the reversal, is 1-3 yr. We have seen four of these events in 40 yr. A model consisting of two successive outbursts in polarized flux density, with EVPAs counterrotating, superposed on a steady polarized jet, can explain many of the details of the observations. Polarization images support this interpretation. The model can also help to explain similar events seen at optical wavelengths. The outbursts needed for the model can be generated by the supermagnetosonic jet model of Nakamura et al. and Nakamura & Meier, which requires a strong helical magnetic field. This model produces forward and reverse pairs of fast and slow MHD waves, and the plasma inside the two fast/slow pairs rotates around the jet axis, but in opposite directions.