A fully three-dimensional (3D) magnetohydrodynamical (MHD) model is applied to simulate the evolution of the large-scale magnetic field in cluster galaxies interacting with the intra-cluster medium (ICM). As the model input we use a time dependent gas velocity field resulting from 3D N-body sticky-particle simulations of a galaxy. The modeled clouds are affected by the ram pressure due to their rapid motion through the ICM in the central part of a cluster. Numerical simulations have shown that after the initial compression phase due to ram pressure a process of gas re-accretion onto the galactic disk takes place. We find that the gas re-accretion leads to an increase of the total magnetic energy without any dynamo action. The simulated magnetic fields are used to construct the model maps of high-frequency (Faraday rotation-free) polarized radio emission. We show that the evolution of the polarized intensity shows features that are characteristic for different evolutionary stages of an ICM-ISM interaction. The comparison of polarized radio continuum emission maps with our model permits to determine whether the galaxy is in the compression or in the re-accretion phase. It also provides an important constraint upon the dynamical modeling of an ICM-ISM interactions.