In this study, the seismic behavior of a recycled aggregate concrete-filled square steel tube (S-RACFST) frame under different design conditions was investigated. Based on previous studies, a finite element model for the seismic behavior of the S-RACFST frame was developed. Moreover, the axial compression ratio, beam–column line stiffness ratio, and yield bending moment ratio of the beam–column were regarded as the variation parameters. It was through these parameters that the seismic behavior of eight S-RACFST frame finite element specimens was discussed. The seismic behavior indexes, such as the hysteretic curve, ductility coefficient, energy dissipation coefficient, and stiffness degradation were obtained—which, in turn, revealed the influence law and the degree of the design parameters regarding seismic behavior. Moreover, the sensitivity of the various parameters with respect to the seismic behavior of the S-RACFST frame was evaluated via grey correlation analysis. The results show that the hysteretic curves of the specimens were fusiform and full with respect to the different parameters. Firstly, with the axial compression ratio increasing from 0.2 to 0.4, the ductility coefficient increased by 28.5%. In addition, the equivalent viscous damping coefficient of the specimen with the axial compression ratio of 0.4 was 17.9% higher than that of the specimen with the axial compression ratio of 0.2, which was 11.5% as well as that with an axial compression ratio of 0.3. Second, when the line stiffness ratio rises from 0.31 to 0.41, the specimens’ bearing capacity and displacement ductility coefficient both get better. However, the displacement ductility coefficient gradually decreases when the line stiffness ratio is greater than 0.41. As a result, an optimal line stiffness ratio (0.41) thus exhibits good energy dissipation capacity. Thirdly, with the increase in the yield bending moment ratio from 0.10 to 0.31, the bearing capacity of the specimens improves. In addition, the positive and negative peak loads increased by 16.4% and 22.8%, respectively. Moreover, the ductility coefficients were all close to three, thus demonstrating good seismic behavior. The stiffness curve of the specimen with a large yield bending moment ratio with respect to the beam–column, is higher than those that possess a small beam–column yield moment ratio. In addition, the yield bending moment ratio of the beam–column possesses a significant influence on the seismic behavior of the S-RACFST frame. Furthermore, the yield bending moment ratio of the beam–column should be considered first in order to ensure the seismic behavior of the S-RACFST frame.