We reveal the mechanism of the noncoaxial rotational Doppler effect (RDE) of an optical vortex and report its application in discriminating the orientation of the rotating axis of the rotating body. In most cases of the RDE-based measurement, the beam axis must be aligned with the rotating axis of the rotational body to observe a good signal. Once the beam axis is not coaxial with the rotating axis, the RDE frequency shift would change related to the misalignment distance, which can be called the noncoaxial RDE. Here, we take the advantage of the misaligned RDE augment with precise light-field modulation and successfully realize the discrimination of the orientation of the rotating axis relative to the illuminating beam. We clarify the principle of noncoaxial RDE and explain why the incomplete optical vortex (OV) is sensitive to the position of the rotating axis. We switch the OV field into four quadrants synchronized with sampling by the data acquisition system, and conduct Fourier transformation of the signals. Combined with the fitting algorithm, the orientation of the rotating axis can be recognized directly. This method may find applications for the noncontact detection of rotating bodies in both industrial and astronomical scenarios.