Anisotropic exchange couplings, such as the Dzyaloshinskii-Moriya interaction (DMI), have played a vital role in the formation and dynamics of spin textures. This work predicts an anisotropic conduction electron spin density in metals with heavy magnetic impurities. The polarization of this Dzyaloshinskii-Moriya spin density (DM-SD) is not collinear to the localized magnetic moments but rotated by the spin-dependent skew scattering of heavy atoms. The DM-SD induces the DMI between magnetic moments in metals and, therefore, it is the anisotropic extension of the Rutherman-Kittel-Kasuya-Yoshida spin density. Our model consists of two localized magnetic moments, one with a large spin-orbit coupling (a lanthanide or rare earth), in a free electron gas. The lanthanide spin controls the DM-SD strength and polarization, promising a flexible control mechanism for anisotropic couplings.