This paper presents the design, optimization, and experimental testing of a new compliant rotary positioning stage with constant torque output. The constant-torque rotary stage is devised based on flexure-based zero-stiffness beams. It exhibits a simpler structure than existing works and is easier to fabricate. Based on the principle of zero-stiffness beam, the dominant parameters are determined by introducing an optimization algorithm. The performance of the rotary stage is verified by executing finite element analysis (FEA) simulation study, which predicts that the designed stage caters for the desired objective. A prototype rotary stage is fabricated by 3D printer for rapid prototyping. Experimental studies are carried out to validate the proposed conceptual design. Repeatability test verifies the stability and feasibility of the designed constant-torque rotary stage.