  We calculate the optically thin synchrotron emission of fast electrons and
positrons in a spiral stationary magnetic field and a radial electric field of
a rotating relativistic strongly magnetized force-free jet consisting of
electron-positron pair plasma. The magnetic field has a helical structure with
a uniform axial component and a toroidal component that is maximal inside the
jet and decreasing to zero towards the boundary of the jet. Doppler boosting
and swing of the polarization angle of synchrotron emission due to the
relativistic motion of the emitting volume are calculated. The distribution of
the plasma velocity in the jet is consistent with the electromagnetic field
structure. Two spatial distributions of fast particles are considered: uniform,
and concentrated in the vicinity of the Alfven resonance surface. The latter
distribution corresponds to the regular acceleration by an electromagnetic wave
in the vicinity of its Alfven resonance surface inside the jet. The
polarization properties of the radiation have been obtained and compared with
the existing VLBI polarization measurements of parsec-scale jets in BL Lac
sources and quasars. Our results give a natural explanation of the observed
bimodality in the alignment between the electric field vector of the polarized
radiation and the projection of the jet axis on the plane of the sky. We
interpret the motion of bright knots as a phase velocity of standing spiral
eigenmodes of electromagnetic perturbations in a cylindrical jet. The degree of
polarization and the velocity of the observed proper motion of bright knots
depend upon the angular rotational velocity of the jet. The observed
polarizations and velocities of knots indicate that the magnetic field lines
are bent in the direction opposite to the direction of the jet rotation.
