Relativistic effects on the radial equilibrium of non-neutral plasmas confined in cylindrical traps are analyzed for rigid and sheared modes of plasma rotation, both with and without the presence of a coaxial inner charged conductor. The changes with respect to the non-relativistic results are especially pronounced for the fast rotational equilibrium solutions. In particular, relativistic effects can limit the plasma outer radius. Analytical estimates of this maximum radius are found both for a rigid plasma rotation and for the case of a uniform plasma density. It is also observed that the Brillouin density limit is modified when the shielding of the external magnetic field by the current associated with the plasma rotation becomes significant.