This study investigated the mechanical properties and stress–strain relationship of polypropylene fiber recycled aggregate concrete (PFRAC) subjected to uniaxial cyclic compression. A total of 78 cylindrical specimens were designed for uniaxial cyclic compression test with coarse aggregate replacement rate, polypropylene fiber volume fraction, and loading rate as variation parameters. The failure process of the specimens under cyclic loading was observed and recorded. The stress–strain curve of PFRAC was summarized. The important mechanical properties of PFRAC were obtained, such as plastic strain, accumulated energy dissipation. The microstructure of PFRAC was analyzed by scanning electron microscopy, and the crack resistance mechanism of PFRAC under cyclic loading was revealed. The results show that the PFRAC under cyclic loading appeared oblique splitting failure. The compressive stress–strain curve envelope of PFRAC subjected to cyclic loading exhibited similarity to the monotonic counterpart. The addition of polypropylene fibers can improve the peak stress, peak strain, residual stress, post‐peak ductility, and accumulated energy dissipation of the recycled concrete. In addition, a constitutive relation formula for the PFRAC stress–strain curve under cyclic loading is proposed, and the fitting result is good.