Jiangwei Xu, Heng Xu, Yanjun Guo, Jinchen Jiang, Bojun Wang, Zihan Xue, Yunpeng Men, Kejia Lee, Bing Zhang, Weiwei Zhu, Jinlin Han

Fast radio bursts (FRBs) are luminous, dispersed millisecond-duration radio bursts whose origin is poorly known. Recent observations suggest that some FRBs may reside in binary systems, even though conclusive evidence remains elusive. Here we report the detection of a 26.24$\pm$0.02 day periodicity in Faraday rotation measure (RM) of an actively repeating source named FRB 20201124A. The detection was made from 3,106 bursts collected with the Five-hundred-meter Aperture Spherical radio Telescope (FAST) over ~365 days. The RM periodicity is coherently phase-connected across ~14 cycles over a 1-year duration. Our detection of RM periodicity corresponds to a natural logarithmic Bayesian factor of 1,168. The detection significances vary between 5.9-34 {\sigma} under different assumptions. Such a periodicity provides evidence for the binary nature of FRB 20201124A, where the periodic RM variations arise from the orbital motion of the FRB source within the magnetoionic environment of the system. Together with previous observations, our result suggests that being in binary systems may be a common feature for actively repeating FRB sources.