The radiative recombination of an unpolarized electron with a polarized highly charged H-like ion in its ground state is studied. The absolute and relative values of the electron spin-flip contribution to the cross section of the process for various scattering angles and photon polarizations are calculated. It is shown that, in addition to the forward and backward directions, there are some other scattering angles of the emitted photon, where, at a fixed linear photon polarization, the spin-flip transition gives a dominant contribution to the differential cross section.