Recycled aggregate concrete (RAC) possesses different mechanical properties than ordinary concrete because of inherent faults in recycled aggregates (RAs), such as the old interfacial transition zone (ITZ). However, the application of nano-SiO2 presents an effective methodology to enhance the quality of RA. In this study, nano-SiO2-modified recycled aggregate (SRA) was used to replace natural aggregate (NA), and the stress–strain relationships and cyclic behavior of nano-SiO2-modified recycled aggregate concrete (SRAC) with different SRA replacement rates were investigated. After evaluating the skeleton curve of SRAC specimens, the existing constitutive models were compared. Additionally, the study also proposed a stress–strain model designed to predict the mechanical behavior of concrete in relation to the SRA replacement rate. The results show that compared with RAC, the axial compressive strength of SRAC specimens showed increases of 40.27%, 29.21%, 26.55%, 16.37%, and 8.41% at specific SRA replacement rates of 0%, 30%, 50%, 70%, and 100%, respectively. Moreover, the study found that the Guo model’s calculated results can accurately predict the skeleton curves of SRAC specimens.