The key information about any nanoscale system relates to the orientations and conformations of its parts. Unfortunately, these details are often hidden below the diffraction limit, and elaborate techniques must be used to optically probe them. Here we present imaging of the 3D rotation motion of metal nanorods, restoring the distinct nanorod orientations in the full extent of azimuthal and polar angles. The nanorods imprint their 3D orientation onto the geometric phase and space-variant polarization of the light they scatter. We manipulate the light angular momentum and generate optical vortices that create self-interference images providing the nanorods' angles via digital processing. After calibration by scanning electron microscopy, we demonstrated time-resolved 3D orientation imaging of sub-100 nm nanorods under Brownian motion (frame rate up to 500 fps). We also succeeded in imaging nanorods as nanoprobes in live-cell imaging and reconstructed their 3D rotational movement during interaction with the cell membrane (100 fps).