A possible periodic RM evolution in the repeating FRB 20220529

Fast radio bursts (FRBs) are mysterious millisecond-duration radio transients of extragalactic origin. Some of them repeat, while others apparently do not. Investigations of periodic activity in repeating FRB have been conducted to probe their origins. While periodicity in the burst rate has been reported, studies of periodicities in other properties, such as dispersion measure (DM) and rotation measure (RM), are sparse. FRB~20220529 was monitored by the Five-hundred-meter Aperture Spherical radio Telescope (FAST) for nearly three years, providing an opportunity to investigate periodicity in its observed properties. Here we report a possible period of $\sim 200$ days in the RM evolution, with a significance of {4.1 $\sigma$} estimated via the Lomb-Scargle algorithm and {3.1 $\sigma$} with the phase-folding method. Periodicity in the burst rate was also investigated. It may indicate that the FRB progenitor is in a binary system, which is consistent with the significant RM increase and prompt recovery of this FRB on a week-timescale. Other scenarios, such as a system with an intermediate-mass black hole, are also explored.