We propose a single-exposure phase-shifting digital holography based on a wave-splitting method using a random-phase reference wave. A random-phase reference wave gives random-phase distribution on the digital hologram. Using the amplitude and the phase distributions of the reference wave, the fully complex amplitude of the object wave is obtained. The proposed method requires not devised optical systems but ordinary imaging devices, such as CCD cameras. A preliminary experimental result is given to confirm the proposed method.