We consider the effective electric polarizability and electric-field–induced birefringence of a dilute solution of rod-like semiflexible charged polymers using hydrodynamic simulations and scaling arguments. We investigate the influence of polymer length, salt concentration, electric field strength and polyion concentration. We show that the polarizabilty is drastically reduced not only for high but also for very low salt concentrations, i.e. when the ionic clouds of neighboring rods start to overlap. As the electric polarizability (favoring rod orientation parallel to the electric field) decreases, the elasto-hydrodynamic orientation due to rod bending (favoring perpendicular alignment) can take over for not too stiff rods. This furnishes a generic mechanism for the experimentally well-known birefringence anomaly of a wide class of charged rod-like systems.