The 23-year-old was last seen at around 00.30am on Saturday 16th January in the Spamount Street area.
Anne Marie is described as being 5’1” tall, of slim build, ruby red hair, blue eyes and was last seen wearing a white long sleeved jumper, blue jeans and black ankle boots.
Anne Marie has a tattoo of a heart locked with a key on the left side of her chest.
Inspector Jamie Hughes said : “We are keen to ensure that Anne Marie is safe and well.
“I would ask Anne Marie or anyone who knows of her whereabouts to contact officers at Tennent Street on 101.”