  We study stationary, electrically charged fluid structures encircling a
rotating compact object with a dipole magnetic field oriented along the
rotation axis. This situation is described in an idealized way by the Kerr
metric and a magnetic dipole "test" field, that does not affect the spacetime.
The self-gravitational and self-electromagnetic field of the fluid are
neglected and the fluid is assumed to be non conductive and in rigid motion.
Our work generalizes a previous study by Kov\'a\v{r} et al.(2016) by taking
into account the rotation of the central object. Therefore, we focus on the
influence of the rotation onto the existence and position of bound fluid
structures. Frame dragging effects allow the existence of polar clouds, which
could not be found in non-rotating case. Furthermore counter-rotating
equatorial tori become more preferred the faster the central object is
spinning.
