Anchoring systems for use in cavity wall structures having an inner wythe and an outer wythe constructed of rubble stone are disclosed. The anchoring system employs an anchor fastened to or set within the inner wythe that extends into the cavity and connects to a J-hook. A vertically adjustable veneer tie enwraps the J-hook, limiting lateral movement and front-to-back displacement, and is set within the bed joint of the outer wythe. The anchoring system minimizes cavity size and provides stability for an uncoursed outer wythe equivalent to that of anchoring systems for standards coursed bed joints.