In this work we present a polarization analysis at radio frequencies of Markarian 421, one of the closest (z = 0.03) TeV blazars. The observations were obtained, both in total and in polarized intensity, with the Very Long Baseline Array (VLBA) at 15, 24, and 43 GHz throughout 2011, with one observation per month (for a total of twelve epochs). We investigate the magnetic field topology and the polarization structure on parsec scale and their evolution with time. We detect polarized emission both in the core and in the jet region, and it varies with frequency, location and time. In the core region we measure a mean fractional polarization of ∼ 1-2%, with a peak of about 4% in March at 43 GHz; the polarization angle is almost stable at 43 GHz, but it shows significant variability in the range 114° - 173° at 15 GHz. In the jet region the polarization properties show a more stable behavior; the fractional polarization is ∼ 16% and the polarization angle is nearly perpendicular to the jet axis. The higher EVPA variability observed at 15 GHz is due both to a variable Faraday rotation effect and to opacity. The residual variability observed in the intrinsic polarization angle, together with the low degree of polarization in the core region, could be explained with the presence of a blend of variable cross-polarized subcomponents within the beam.