A masonry connector for a veneer wall has an outer coupling end for connection to a wall tie secured to the veneer. An inner anchoring end of the connector is secured to the back-up wall. Where the back-up wall is masonry wall, the anchoring portion includes a vertical plate, apertured to be keyed into the mortar between two side-by-side, adjacent blocks of the back-up wall, and a laterally projecting, corrugated flange to be keyed into the mortar between two vertically adjacent blocks. A rearwardly facing edge immediately in front of the anchoring end abuts against the outer face of the masonry wall to ensure the positioning of the connector at the proper depth. A low conductivity section of the connector between the coupling end and the anchoring end has a series of holes through it to minimize the thermal transfer along the connector.