The discovery of the optical rotational Doppler effect associated with orbital angular momentum of light paves a new way to detect the rotational speed of spinning objects. In this paper, we investigate the influence of lateral misalignment, i.e., the distance between the beam axis of a probe light and the rotation axis of a spinning object, on the rotational Doppler effect. First, we analyze the mechanism of the rotational Doppler effect of optical vortices based on the linear Doppler effect. Specifically, we consider the general case where the center of the optical vortex does not coincide with the rotation axis, and deduce the generalized formula of rotational Doppler shift based on a local scattering model. It is found that the bandwidth of the rotational Doppler signal depends proportionally on the amount of lateral misalignment, whereas the value of rotational Doppler shift remains constant. A proof-of-concept experiment is performed, and the measured results agree well with theoretical predictions. These findings may be useful for practical application of the optical rotational Doppler effect in remote sensing and metrology.