We investigate, for the first time at z~3, the clustering properties of 189 Type 1 and 157 Type 2 X-ray active galactic nuclei (AGNs) of moderate luminosity (left angle bracketL sub(bol)right angle bracket = 10 super(45.3) erg s super(-1)), with photometric or spectroscopic redshifts in the range 2.2 < z < 6.8. This result requires a drop in the halo masses of Type 1 and 2 COSMOS AGNs at z ~ 3 compared to z lap 2 XMM-COSMOS AGNs with similar luminosities. A model which assumes that the AGNs activity is triggered by major mergers is quite successful in predicting both the low halo mass of COSMOS AGNs and the typical mass of luminous SDSS quasars at z~3, with the latter inhabiting more massive halos respect to moderate luminosity AGNs. Following our clustering measurements, we argue that this fast BH growth at z~3 in AGNs with moderate luminosity occurs in DMHs with typical mass of ~ 6x 10 super(12) h super(-1) M sub(middot in circle).