We measure the clustering of nonquasar X-ray active galactic nucleus (AGN) at z = 0.7-1.4 in the AEGIS field. Using the cross-correlation of 113 Chandra-selected AGN, with a median log L X = 42.8 erg s −1 , with ∼5000 DEEP2 galaxies, we find that the X-ray AGNs are fitted by a power law with a clustering scale length of r 0 = 5.95 ± 0.90 h −1 Mpc and slope γ = 1.66 ± 0.22. X-ray AGNs have a similar clustering amplitude as red, quiescent and "green" transition galaxies at z ∼ 1 and are significantly more clustered than blue, starforming galaxies. The X-ray AGN clustering strength is primarily determined by the host galaxy color; AGNs in red host galaxies are significantly more clustered than AGNs in blue host galaxies, with a relative bias that is similar to that of red to blue DEEP2 galaxies. We detect no dependence of clustering on optical brightness, X-ray luminosity, or hardness ratio within the ranges probed here. We find evidence for galaxies hosting X-ray AGN to be more clustered than a sample of galaxies with matching joint optical color and magnitude distributions. This implies that galaxies hosting X-ray AGN are more likely to reside in groups and more massive dark matter halos than galaxies of the same color and luminosity without an X-ray AGN. In comparison to optically selected quasars in the DEEP2 fields, we find that X-ray AGNs at z ∼ 1 are more clustered than optically selected quasars (with a 2.6σ significance) and therefore may reside in more massive dark matter halos. Our results are consistent with galaxies undergoing a quasar phase while in the blue cloud before settling on the red sequence with a lower-luminosity X-ray AGN, if they are similar objects at different evolutionary stages.