The utilization of recycled aggregate (RCA) in preparing recycled concrete (RAC) is an effective measure to solve the increase in construction waste. Furthermore, applying RAC to flexural members is a viable practice. The addition of steel fiber to RAC to prepare steel fiber recycled concrete (SFRAC) solves the performance deterioration caused by the recycled aggregate, so it is necessary to study the effects of the recycled aggregate replacement rate and fiber–volume ratio on the crack resistance and bending performance of SFRAC beams. In this study, 13 beams were designed and manufactured, with the water–cement ratio, recycled aggregate replacement rate, and fiber–volume ratio as the primary variables, and the cracking moment and ultimate moment of the SFRAC beams were systematically studied. The results show that the cracking and ultimate moments of the SFRAC beams increased with decreases in the water–cement ratio or with increases in the fiber–volume ratio and were unaffected by the replacement rate of recycled aggregates. Based on the experimental results and theoretical analysis, a calculation model and formula for the cracking moment were established. The ultimate bearing capacity of SFRAC beams can be accurately determined using the ACI 318 and ACI 544 standards. The research results serve as a valuable reference for the design of SFRAC beams, effectively address the issue of performance degradation in RAC structural members, and promote the use of green building materials.