Precision angular sensing is an essential technology in physical experiments. Unlike length sensing with a laser beam, it has been thought that sensitivity to the angular motion cannot be enhanced with the help of an optical cavity. A method of angular signal amplification using an optical cavity, called the cavity-amplified angular sensor (CAAS), is proposed. By adjusting or compensating for the Gouy phase of the cavity, the electric field of the laser generated in proportion to the target rotation is coherently stacked in the proposed method. The advantage of this method over other angular sensors is its high sensitivity with the small sensing spot size. Three possible optical configurations are considered, of which two experimentally available ones are investigated. The angular signal amplification is demonstrated for both of them. Based on the theoretical calculation for a realistic model, the fundamental angular sensing noise level is expected to be as low as 10-15rad/Hz1/2, with a 1 mm laser beam size and 10 mW laser power.