This paper presents a new method of gaining spatial resolution in continuous wave (CW) Doppler radars by using a vibrating antenna. Resolution of direction finding, though conventionally controlled through beam steering or other circuitry, is decoupled from the antenna and front-end circuitry by vibrating the antenna in a controlled fashion. It is shown that vibrating an antenna results in an induced Doppler shift, whereby the return from each spatial angle has a different Doppler frequency. This allows for smaller aperture antennas or antenna arrays to be used in place of larger aperture antennas or antenna arrays, thereby reducing the overall system's size and complexity. As a proof of concept, a single vibrating antenna radar is designed, fabricated, and tested in order to verify the angle finding capability for a single, as well as multiple targets. This method may also be expanded into two-dimensional detection by integrating a vibrating one-dimensional array.