We present the measurement of the two-point cross-correlation function (CCF) of 8198 Sloan Digital Sky Survey Data Release 7 quasars and 349,608 Data Release 10 CMASS galaxies from the Baryonic Oscillation Spectroscopic Survey at 0.3 < z < 0.9. The CCF can be reasonably well fit by a power-law model ξQG(r) = (r/r 0)–γ on projected scales of rp = 2-25 h –1 Mpc with r 0 = 6.61 ± 0.25 h –1 Mpc and γ = 1.69 ± 0.07. We estimate a quasar linear bias of bQ = 1.38 ± 0.10 at langzrang = 0.53 from the CCF measurements, which corresponds to a characteristic host halo mass of ~4 × 1012 h –1 M ☉, compared with a ~1013 h –1 M ☉ characteristic host halo mass for CMASS galaxies. Based on the clustering measurements, most quasars at \bar{z}\sim 0.5 are not the descendants of their higher luminosity counterparts at higher redshift, which would have evolved into more massive and more biased systems at low redshift. We divide the quasar sample in luminosity and constrain the luminosity dependence of quasar bias to be dbQ /dlog L = 0.20 ± 0.34 or 0.11 ± 0.32 (depending on different luminosity divisions) for quasar luminosities –23.5 > Mi (z = 2) >–25.5, implying a weak luminosity dependence of clustering for luminous quasars at \bar{z}\sim 0.5. We compare our measurements with theoretical predictions, halo occupation distribution (HOD) models, and mock catalogs. These comparisons suggest that quasars reside in a broad range of host halos. The host halo mass distributions significantly overlap with each other for quasars at different luminosities, implying a poor correlation between halo mass and instantaneous quasar luminosity. We also find that the quasar HOD parameterization is largely degenerate such that different HODs can reproduce the CCF equally well, but with different satellite fractions and host halo mass distributions. These results highlight the limitations and ambiguities in modeling the distribution of quasars with the standard HOD approach.