Haran Bazoglu, 38 was reported missing at about 4pm on Saturday November 20 2021 having last been seen in the Willesborough area of the town.
Officers are concerned for his welfare and urging anyone who may see him to get in touch.
Mr Bazoglu is described as having black/brown hair and wearing a black jacket. He is known to specifically use public transport.
Anyone who may have information is asked to contact Kent Police on 101 quoting 20-0929.