We study the polarization properties of synchrotron self-Compton (SSC) emission for an isotropic electron distribution in an axisymmetric magnetic field, as a function of the electron energy and the viewing angle. Despite the opposite contributions of the unpolarized and polarized components of synchrotron radiation, a large fraction of the synchrotron polarization can be preserved. If the magnetic field is uniform, the degree of SSC polarization can be very high, reaching values up to 40 per cent. Such a high polarization is within the measurement capabilities of the present generation of X-ray polarimeters. The polarization vector is found to be parallel to the synchrotron one, which in turn is perpendicular or parallel to the magnetic field axis, depending on the magnetic field distribution. Simultaneous, multiwavelength polarization measurements can therefore provide an important test for the SSC model.