We study the spatial clustering through the projected two-point correlation function of $632$ $(1130)$ XMM-COSMOS Active Galactic Nuclei (AGNs) with known spectroscopic (spectroscopic or photometric) redshifts in the range $z = [0.1 - 2.5]$ in order to measure the AGN bias and estimate the typical mass of the hosting dark matter (DM) halo as a function of AGN host galaxy properties. We create AGN subsamples in terms of stellar mass $M_*$ and specific black hole accretion rate $L_X/M_*$, to probe how AGN environment depends on these quantities. For the full spectroscopic AGN sample, we measure a typical DM halo mass of $log (M_mathrm{halo} / h^{-1}mathrm{M}_odot)= 12.79_{-0.43}^{+0.26}$, similar to galaxy group environments and in line with previous studies for moderate-luminosity X-ray selected AGN. We find no significant dependence on $L_X/M_*$, with $log (M_mathrm{halo} / h^{-1}mathrm{M}_odot) = 13.06_{-0.38}^{+0.23}$ ($12.97_{-1.26}^{+0.39}$) for the low (high) $L_X/M_*$ subsample. We also find no difference in the hosting halos in terms of $M_*$ with $log (M_mathrm{halo} / h^{-1}mathrm{M}_odot) = 12.93_{-0.62}^{+0.31}$ ($12.90_{-0.62}^{+0.30}$) for the low (high) $M_*$ subsample. By comparing the $M_*-M_mathrm{halo}$ relation derived for XMM-COSMOS AGN subsamples with what is expected for normal non-active galaxies by abundance matching and clustering results, we find that the typical DM halo mass of our high $M_*$ AGN subsample is similar to that of non-active galaxies. However, AGNs in our low $M_*$ subsample are found in more massive halos than non-active galaxies. By excluding AGNs in galaxy groups from the clustering analysis, we find evidence that the result for low $M_*$ may be due a larger fraction of AGNs as satellites in massive halos.