We propose a new approach capable of measuring local seismic anisotropy from 6C (three-component translation and three-component rotation) amplitude observations of ambient seismic noise data. Our recent theory demonstrates that the amplitude ratio of 6C cross-correlation functions (CCFs) enables retrieving the local phase velocity. This differs from conventional velocity extraction methods based on travel time. Its local sensitivity kernel beneath the 6C seismometer allows us to study anisotropy from azimuth-dependent CCFs, avoiding path effects. Such point measurements have great potential in planetary exploration, ocean bottom observations, or volcanology. We apply this approach to a small seismic array at Pinon Flat Observatory (PFO) in southern California, array-deriving retrieves rotational ground motions from microseismic noise data. The stress and structure-induced anisotropy is well resolved and compatible with other tomography results, providing constraints on the origin of depth-dependent seismic anisotropy.