We study exact stationary and axisymmetric solutions describing charged rotating black holes localized on a 3-brane in the Randall-Sundrum braneworld. The charges of the black holes are considered to be of two types, the first being an induced tidal charge that appears as an imprint of nonlocal gravitational effects from the bulk space and the second is a usual electric charge arising due to a Maxwell field trapped on the brane. We assume a special ansatz for the metric on the brane taking it to be of the Kerr-Schild form and show that the Kerr-Newman solution of ordinary general relativity in which the electric charge is superseded by a tidal charge satisfies a closed system of the effective gravitational field equations on the brane. It turns out that the negative tidal charge may provide a mechanism for spinning up the black hole so that its rotation parameter exceeds its mass. This is not allowed in the framework of general relativity. We also find a new solution that represents a rotating black hole on the brane carrying both charges. We show that for a rapid enough rotation the combined influence of the rotational dynamics and the local bulk effects of the "squared" energy-momentum tensor on the brane distort the horizon structure of the black hole in such a way that it can be thought of as composed of nonuniformly rotating null circles with growing radii from the equatorial plane to the poles. We finally study the geodesic motion of test particles in the equatorial plane of a rotating black hole with tidal charge. We show that the effects of negative tidal charge tend to increase the horizon radius, as well as the radii of the limiting photon orbit, the innermost bound and the innermost stable circular orbits for both direct and retrograde motions of the particles.