Recent advances in high-harmonic generation gave rise to soft X-ray pulses with higher intensity, shorter duration and higher photon energy. One of the remaining shortages of this source is its restriction to linear polarization, since the yield of generation of elliptically polarized high harmonics has been low so far. We here show how this limitation is overcome by using a cross-polarized two-colour laser field. With this simple technique, we reach high degrees of ellipticity (up to 75%) with efficiencies similar to classically generated linearly polarized harmonics. To demonstrate these features and to prove the capacity of our source for applications, we measure the X-ray magnetic circular dichroism (XMCD) effect of nickel at the M-2,M-3 absorption edge around 67 eV. There results open up the way towards femtosecond time-resolved experiments using high harmonics exploiting the powerful element-sensitive XMCD effect and resolving the ultrafast magnetization dynamics of individual components in complex materials.