This paper presents a study that uses only a single microphone for direction of arrival (DOA) estimation, as opposed to a microphone array. The proposed method utilises a circularly moving microphone; exploiting the Doppler effect produced by the motion along the circular path to find the DOA. Being inspired by a previous study which utilised a microphone array with circular sampling, the change in instantaneous frequency of the signal is estimated using the Centre of Gravity algorithm. The method is tested by both numerical simulations and practical experiments. A practical recording device that has a rotating disc with a microphone embedded was designed, developed, and utilised for the experiments. The results suggest the DOA can be estimated accurately when the frequency of the sound source is high.