We study the cross-correlation between 716 Mg II quasar absorption systems and $\sim 100,000$ Luminous Red Galaxies (LRGs) selected from the Sloan Digital Sky Survey Data Release 3 in the redshift range $0.4\!\leq\!z\!\leq\!0.8$. The Mg II systems were selected to have $\lambda\lambda$ 2796 & 2803 rest-frame equivalent widths $\geq\!1.0$$\AA\$ and identifications confirmed by the FeII$\lambda 2600$ or MgI$\lambda 2852$ lines. Over co-moving scales 0.2–13$h^{-1}{\rm \,Mpc}$, the MgII–LRG cross-correlation has an amplitude $0.69 \pm 0.09$ times that of the LRG–LRG auto-correlation. Since LRGs have halo-masses of $10^{13}$ M$_{\odot}$, this strong cross-correlation signal implies that the absorber host-galaxies have halo-masses $1-2\times 10^{12}$ M$_{\odot}$.