  We analytically investigate the pertubative effects of a quantum
conformally-coupled scalar field on rotating (2+1)-dimensional black holes and
naked singularities. In both cases we obtain the quantum-backreacted metric
analytically. In the black hole case, we explore the quantum corrections on
different regions of relevance for a rotating black hole geometry. We find that
the quantum effects lead to a growth of both the event horizon and the
ergosphere, as well as to a reduction of the angular velocity compared to their
corresponding unperturbed values. Quantum corrections also give rise to the
formation of a curvature singularity at the Cauchy horizon and show no evidence
of the appearance of a superradiant instability. In the naked singularity case,
quantum effects lead to the formation of a horizon that hides the conical
defect, thus turning it into a black hole. The fact that these effects occur
not only for static but also for spinning geometries makes a strong case for
the r\^ole of quantum mechanics as a cosmic censor in Nature.
