We prove that every subgroup of p-power index in a right-angled Artin group is conjugacy p-separable. In particular, every right-angled Artin group is conjugacy p-separable. A consequence of this result is that the outer automorphism group of a right-angled Artin group is virtually residually p-finite. Another consequence of this result is that the outer automorphism group of a right-angled Artin group is K-residual, where K is the class of all outer automorphism groups of finite p-groups. We also prove that the Torelli group of a right-angled group is residually torsion-free nilpotent, hence residually p-finite and bi-orderable.