We test the reliability of a method to measure the mean halo mass of absorption-line systems such as damped Lyα absorbers (DLAs). The method is based on measuring the ratio of the cross-correlation between DLAs and galaxies to the autocorrelation of the galaxies themselves, which is (in linear theory) the ratio of their bias factor . We show that the ratio of the projected cross- and autocorrelation functions [wdg(rθ)/wgg(rθ)] is also the ratio of their bias factor, irrespective of the galaxy distribution, provided that one uses the same galaxies for wdg(rθ) and wgg(rθ). Thus, the method requires only multiband imaging of DLA fields and is applicable to all redshifts. Here, we focus on z = 3 DLAs. We demonstrate that the method robustly constrains the mean DLA halo mass using smoothed particle hydrodynamics (SPH) cosmological simulations that resolve DLAs and galaxies in halos of mass Mh 5.2 × 1010 M. If we use the bias formalism of Mo & White with the DLA and galaxy mass distributions of these simulations, we predict an amplitude ratio wdg/wgg of 0.771. Direct measurement of these correlation functions from the simulations yields wdg/wgg = DLA/gal = 0.73 ± 0.08, in excellent agreement with that prediction. Equivalently, inverting the measured correlation ratio to infer the (logarithmically) averaged DLA halo mass yields log MDLA(M) = 11.13, in excellent agreement with the true value in the simulations: log MDLA(M) = 11.16 is the probability-weighted mean mass of the DLA host halos in the simulations. The cross-correlation method thus appears to yield a robust estimate of the average host halo mass, even though the DLAs and the galaxies occupy a broad mass spectrum of halos and massive halos contain multiple galaxies with DLAs. If we consider subsets of the simulated galaxies with high star formation rates (representing Lyman break galaxies [LBGs]), then both correlations are higher, but their ratio still implies the same DLA host mass, irrespective of the galaxy subsamples, i.e., the cross-correlation technique is also reliable. The inferred mean DLA halo mass, log MDLA = 11.13, is an upper limit, since the simulations do not resolve halos less massive than ~1010.5 M. Thus, our results imply that the correlation length between DLAs and LBGs is predicted to be at most ~2.85 h-1 Mpc, given that z = 3 LBGs have a correlation length of r0 4 h-1 Mpc. While the small size of current observational samples does not allow strong conclusions, future measurements of this cross-correlation can definitively distinguish models in which many DLAs reside in low-mass halos from those in which DLAs are massive disks occupying only high-mass halos.