Zero-shot 3D visual grounding (3DVG) aims to localize a referred object in a 3D scene without task-specific grounding supervision. Existing training-free methods commonly reason over object categories, centers, and bounding boxes, but these representations do not encode the local reference frames needed to interpret viewpoint-dependent expressions such as left of, behind, or facing the door. We propose OriGround, an orientation-aware neuro-symbolic framework that explicitly models object-centric orientations and infers observer viewpoints for zero-shot 3DVG. OriGround parses each query into a viewpoint-aware symbolic program, estimates object-centric orientation bases from multi-view observations, performs anchor- and observer-specific geometric relation scoring, and constructs a reference-frame-aligned visual prompt for final VLM-based disambiguation. On Nr3D, OriGround improves over the strongest training-free baseline by 8.4 points in overall accuracy, with larger gains of 8.9 points on hard queries and 5.6 points on view-dependent queries. On ScanRefer, OriGround further improves overall Acc@0.5 by 17.3 points over VLM-Grounder. Project page: https://origround.github.io/