The use of construction waste for concrete is an effective way to reduce the environmental burden while improving the sustainability of construction materials. Nano-SiO2 (NS) has excellent volcanic ash activity, which can effectively improve the strength of concrete. In this study, the synergistic effects of NS and 30% recycled concrete aggregate (RCA) on the mass loss, compressive strength, ultrasonic sound velocity values and microstructure of RAC after 25, 50, 75 and 100 repetitions of a dry–wet cycle (DWC) of sulfuric acid were investigated. The results show that NS has a significant role in improving RAC performance. The RAC specimens showed the lowest mass loss rate, the highest compressive strength, the lowest ultrasonic velocity value and the best resistance to sulfate erosion when the NS doping was 4%. Meanwhile, under CT and SEM, RAC with NS has lower porosity and higher hydration, which can effectively inhibit the crack generation and has stable volume growth within 0–50 repetitions of DWC. In addition, the addition of NS improves not only the microstructure of the substrate but also the interfacial transition zone (ITZ). When 4% NS was added, the porosity was the lowest and the durability improvement was the best performance. This study not only improves the production performance of RAC but also provides a strong reference for the integrated application of nanomaterials in concrete.