  We calculate the spectral function $A_\rho$ of the $\rho$ meson in nuclear
matter. The calculation is performed in the {\it low density} approximation,
where the in-medium self energy $\Sigma_{med}$ is completely determined by the
vacuum $\rho N$ forward scattering amplitude. This amplitude is derived from a
relativistic resonance model. In comparison to previous non-relativistic
calculations we find a much weaker momentum dependence of $\Sigma_{med}$,
especially in the transverse channel. Special attention is paid to
uncertainties in the model. Thus, we compare the impact of different coupling
schemes for the $RN\rho$ interaction on the results and discuss various
resonance parameter sets.
