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Magnetars are highly magnetized neutron stars that are characterized byrecurrent emission of short-duration bursts in soft gamma-rays/hard X-rays.Recently, FRB 200428 were found to be associated with an X-ray burst from aGalactic magnetar. Two fast radio bursts (FRBs) show mysterious periodicactivity. However, whether magnetar X-ray bursts are periodic phenomena isunclear. In this paper, we investigate the period of SGR 1806-20 activity. Morethan 3000 short bursts observed by different telescopes are collected,including the observation of RXTE, HETE-2, ICE and Konus. We consider theobservation windows and divide the data into two sub-samples to alleviate theeffect of unevenly sample. The epoch folding and Lomb-Scargle methods are usedto derive the period of short bursts. We find a possible period about $ 398.20\pm 25.45 $ days. While other peaks exist in the periodograms. If the period isreal, the connection between short bursts of magnetars and FRBs should beextensively investigated.

Possible periodic activity in the short bursts of SGR 1806-20: connection to fast radio bursts