The effect of a weakly tilted magnetic field perturbations on the equilibrium of a nonneutral plasma confined in a Malmberg-Penning trap is analyzed. A constraint is introduced, that in combination with the Poisson equation allows to select admissible plasma equilibria in the trap in the presence of a non-uniform and a non-axisymmetric magnetic field. Longitudinal plasma currents (analogous to the Pfirsch-Schlüter currents in Tokamaks) appearing in a nonneutral plasma even in the absence of magnetic drifts are explicitly computed in the case of a uniformly tilted magnetic field.