The r-process enrichment in the Galaxy still remains elusive with regard to its nucleosynthesis conditions and the astrophysical sites where it occurs. As part of ongoing efforts to pinpoint the origin of chemically peculiar r-process-enhanced (RPE) stars, we concentrate in this study on the kinematics of RPE stars to investigate possible variations in the r-process enrichment among the Galactic components. We calculate the orbital parameters of a sample of 472 metal-poor RPE stars and associate them to the Galactic bulge, disk and halo populations using a physically motivated classification based on apocenter distance and maximum absolute vertical height of the orbit. We show that the Toomre diagram does not properly separate stars in the disk and halo components when they are on highly eccentric and/or retrograde orbits. The Galactic disk and halo share a similar fraction of RPE stars, in contrast to the earlier perception that the majority of RPE stars belong to the halo. Most of the RPE stars are located within the mixed zone of the action-space diagram, with only about 10% exhibiting clear accretion-like dynamics. The inner disk, inner halo and outer halo stars exhibit similar abundance trends for the n-capture elements.