Vision-language models (VLMs) can detect that an object has rotated across views, but cannot reliably tell by how much. We introduce OR-Bench, a fine-grained benchmark for object-rotation reasoning with eight tasks covering rotation detection, rotation magnitude estimation, and multi-view rotation reasoning. Across 12 VLMs, the gap is stark: the strongest models approach 100% accuracy on detection, yet even coarse magnitude estimation is near chance. When asked for exact angles, models place 91.8--100% of their predictions on just $0^\circ$, $90^\circ$, and $180^\circ$, a failure we term canonical-angle collapse. This collapse persists even without visual input. Representation probing shows that missing information is only part of the explanation. Although rotation information becomes less recoverable at finer granularity, substantial coarse-grained information remains, and a simple linear probe outperforms the models' generated answers. This suggests that VLMs underuse rotation information they already encode. We therefore propose RotationCue, a lightweight decoder that recovers coarse rotation information from the VLM's own frozen representations and feeds it back to the model as intermediate textual context. Across three VLMs, RotationCue improves every model--task combination on OR-Bench, raising macro-average accuracy by 7.9--12.6 points while preserving general capabilities.

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