We present and validate a novel semi-analytical approach to study the effect of dynamical friction (DF) on the orbits of massive perturbers in rotating stellar discs. We find that DF efficiently circularizes the orbit of co-rotating perturbers, while it constantly increases the eccentricity of counter-rotating ones until their angular momenta reverse, then once again promoting circularization. Such ‘drag toward circular co-rotation’ could shape the distribution of orientations of kinematically decoupled cores in disc galaxies, naturally leading to the observed larger fraction of co-rotating cores.