  In this work, we study circular motions of charged particles and their
polarized images around the Kerr black hole immersed in a weak magnetic field.
We pay special attention to the case that both the magnetic field and the
charge-to-mass ratio are not big, thus the effective potential along the radial
motion reduce to a cubic form approximately so that we can express the radius
of the innermost stable circular orbit analytically in terms of the energy and
angular momentum of charged particles. Moreover, we computed the polarized
synchrotron radiations of these particles and obtained the polarized images
semi-analytically for various spins, observational angles and prograde and
retrograde orbits. In particular, We find that these parameters have
significant impacts on the polarization rotation and the magnitude of the
polarization flux.
