The recent experimental discovery of three-dimensional (3D) materials hosting a strong Rashba spin-orbit coupling calls for the theoretical investigation of their transport properties. Here we study the zero-temperature dc conductivity of a 3D Rashba metal in the presence of static diluted impurities. We show that, at variance with the two-dimensional case, in 3D systems, spin-orbit coupling affects dc charge transport in all density regimes. We find in particular that the effect of spin-orbit interaction strongly depends on the direction of the current, and we show that this yields strongly anisotropic transport characteristics. In the dominant spin-orbit coupling regime where only the lowest band is occupied, the conductivity anisotropy is governed entirely by the anomalous component of the renormalized current. We propose that measurements of the conductivity anisotropy in bulk Rashba metals may give a direct experimental assessment of the spin-orbit strength.