High-finesse optical cavity assisted quantum nondemolition (QND) measurement is an important method of generating high-gain spin or momentum squeezed states, which can enhance the sensitivity of atom interferometers beyond the standard quantum limit. Conventional two-mirror Fabry-Perot cavities have the drawback of a standing wave pattern, leading to inhomogeneous atom-light coupling and subsequent degradation of metrological gain. In this study, we present a novel method of achieving homogeneous quantum nondemolition measurement by using an optical ring cavity to generate momentum squeezed states in atom interferometers. We design and develop a high-finesse ($ {\cal{F}} = 2.4(1) \times 10^{4} $), high-vacuum compatible ($ 1\times 10^{-10} \;{\rm mbar}$) optical ring cavity. It utilizes the properties of traveling wave fields to address the issue of inhomogeneous atom-light interaction. A strontium cold atomic ensemble is prepared and coupled into the cavity mode; the nondemolition measurement of atom number is achieved by extracting the dispersive cavity phase shift caused by the passage of atoms through differential Pound-Drever-Hall measurement. Experimental results indicate that under a probe laser power value of 20 μW, the dispersive phase shift of the ring cavity is measured to be 40 mrad. The effective number of atoms coupled into the cavity mode is around $ 1 \times 10^{5} $. The consistency between the ring cavity dispersive phase shift and QND measurement theory is verified by adjusting parameters such as matching the atomic position with the cavity mode and tuning the frequency of the probe laser. The optical ring cavity developed in this work provides an important method for generating spin or momentum squeezed states in atom interferometers. Therefore it holds promise for enhancing their sensitivity, and it is expected to be widely applied to cavity-enhanced quantum precision measurements.