Light curves for more than century optical photometric observations of the blazar OJ 287 reveals strong flares with a quasi-period of about 12 years. For a long time, this period has been interpreted by processes in a binary black hole system. We propose an alternative explanation for this period, which is based on Doppler factor periodic variations of the emitting region caused by jet helicity. Using multi-epoch very large baseline interferometry (VLBI) observations carried out in a framework of the MOJAVE (Monitoring Of Jets in Active galactic nuclei with VLBA Experiments) program and other VLBA (Very Long Baseline Array) archival experiments at the observing frequency of 15 GHz, we derived geometrical parameters of the jet helix. To reach an agreement between the VLBI and photometric optical observation data, the jet component motion at a small angle to the radial direction is necessary. Such non-radial motion is observed and, together with the jet helical shape, can be naturally explained by the development of the Kelvin–Helmholtz instability in the parsec-scale outflow. In this case, the true precession of the OJ 287 jet may manifest itself in differences between the peak flux values of the 12-year optical flares. A possibility to create this precession due to Lense–Thirring effect of a single supermassive black hole is also discussed.