Previous investigations devoted to non-spherical nanoparticles for biosensing have primarily addressed two hot topics, namely, finding nanoparticles with the best shape for refractive index sensing properties and the optimization of size parameters. In this study, based on these hot topics, Au-Ag alloy nanoparticles with excellent optical properties were selected as the research object. Targeting rotationally symmetric Au-Ag alloy nanoparticles for biosensing applications, the complex media function correction model and T-matrix approach were used to systematically analyze the variation patterns of extinction properties, refractive index sensitivity, full width at half maximum, and figure of merit of three rotationally symmetric Au-Ag alloy nanoparticles with respect to the size of the particles and the Au molar fraction. In addition, we optimized the figure of merit to obtain the best size parameters and Au molar fractions for the three rotationally symmetric Au-Ag alloy nanoparticles. Finally, the range of dimensional parameters corresponding to a figure of merit greater than 98% of its maximum value was calculated. The results show that the optimized Au-Ag alloy nanorods exhibit a refractive index sensitivity of 395.2 nm/RIU, a figure of merit of 7.16, and a wide range of size parameters. Therefore, the optimized Au-Ag alloy nanorods can be used as high-performance biosensors. Furthermore, this study provides theoretical guidance for the application and preparation of rotationally symmetric Au-Ag alloy nanoparticles in biosensing.