  We investigate the response of a relativistic plasma to electromagnetic
fields in the framework of the Boltzmann equation incorporating a collision
term in the relaxation rate approximation selected in a form assuring current
conservation. We obtain an explicit solution for the linearized perturbation of
the Fermi-Dirac equilibrium distribution in terms of the average relaxation
rate $\kappa$. We study the resulting covariant, gauge invariant, and current
conserving form of the polarization tensor in the ultrarelativistic and
non-relativistic limits. We evaluate the susceptibility in the
ultrarelativistic limit and explore their dependence on $\kappa$. Finally, we
study the dispersion relations for the longitudinal and transverse poles of the
propagator. We show that for $\kappa> 2\omega_p$, where $\omega_p$ is the
plasma frequency, the plasma wave modes are overdamped. In the opposite case,
$\kappa \ll \omega_p$, the propagating plasma modes are weakly damped.
