The vortex electromagnetic (EM) wave with orbital angular momentum (OAM) brings a new degree of freedom for synthetic aperture radar (SAR) imaging, although to date, its application to multi-input multi-output (MIMO) SAR has not yet been widely reported. In this paper, an orbital angular momentum (OAM)-based MIMO-SAR system is proposed. The rotational Doppler Effect (RDE) of vortex EM waves offers a novel scheme for an OAM-based MIMO-SAR system. By transmitting the rotational vortex EM waves, echoes of different OAM modes can be discriminated by a bandpass filter in the range-Doppler domain. The performance of the proposed scheme is independent of the time-variant channel responses, and the wider beam width of the vortex EM waves delivers, for the same antenna aperture size, better performance in terms of swath width and azimuth resolution, in contrast to the plane EM waves. Moreover, the spatial diversity of vortex EM waves shows great potential to enhance the MIMO-SAR system applications, which involve high-resolution wide-swath remote sensing, 3-D imaging, and radar-communication integration. The proposed scheme is verified by proof-of-concept experiments. This work presents a new application of vortex EM waves, which facilitates the development of new-generation and forthcoming SAR systems.