Aims. We present a multifrequency, dense radio monitoring program of the blazar OJ 287 using the 100-m Effelsberg radio telescope. The program aims to test different binary supermassive black hole (SMBH) scenarios and studying the physical conditions in the central region of this bright blazar. Here, we analyze the evolution in total flux density, linear and circular polarization as a means to study the OJ 287 jet structure and its magnetic field geometry. Methods. We used a recently developed, high-precision data analysis methodology to recover all four Stokes parameters. We measured the total flux density of OJ 287 at nine bands from 2.64 GHz to 43 GHz, the linear polarization parameters at four bands between 2.64 GHz and 10.45 GHz, and the circular polarization at two bands, 4.85 GHz and 8.35 GHz. The mean cadence of our measurements is ten days. Results. Between December 2015 and January 2017 (MJD 57370–57785), OJ 287 showed flaring activity and complex linear and circular polarization behavior. The radio electric vector position angle (EVPA) showed a large clockwise (CW) rotation by ∼340° with a mean rate of −1.04°/day. Based on concurrent very long baseline interferometric (VLBI) polarization data at 15 GHz and 43 GHz, the rotation seems to originate within the jet core at 43 GHz (projected angular size ≤0.15 mas or 0.67 pc at the redshift of the source). Moreover, optical polarization data show a similar monotonic CW rotation with a rate of about −1.1°/day which is superposed with shorter and faster rotations that exhibit rates of about 7.8°/day, mainly in the CW sense. Conclusions. The flux density and polarization variability of the single dish, VLBI and optical data is consistent with a polarized emission component propagating on a helical trajectory within a bent jet. We constrained the helix arc length to 0.26 pc and radius to ≤0.04 pc as well as the jet bending arc length projected on the plane of the sky to ≤1.9–7.6 pc. A similar bending has been observed also in high angular resolution VLBI images of the OJ 287 jet at its innermost regions. The helical trajectory covers only a part of the jet width, possibly its spine. In addition, our results indicate the presence of a stable polarized emission component. Its EVPA (−10°) is oriented perpendicular to the large scale jet, suggesting dominance of the poloidal magnetic field component. Finally, the EVPA rotation begins simultaneously with an optical flare and hence the two might be physically connected. That optical flare has been suggested to be linked to the interaction of a secondary SMBH with the inner accretion disk or originating in the jet of the primary.