The three men, one armed with a knife, entered the man's home in Somerset Gardens, Ayr, at around 8.30am on Wednesday.
They stole the 37-year-old victim's mobile phone before leaving the scene.
Detective Sergeant Jane Hogg, of Ayrshire CID, said: "I would like to take this opportunity to emphasise to members of the public to be extremely cautious when opening your door if you are not expecting any visitors, even those who purport to be police officers.
"We are encouraging anyone who may have seen any of the three men that fit this description in or around the area at the time of the incident to get in contact.
"We are also appealing for anyone that may have CCTV or dash-cam footage from the surrounding streets."
The man dressed in police uniform is aged in his early 30s, around 5ft 10, of a stocky build, and was wearing a black T-shirt under a police vest. He had glasses and spoke with a Scottish accent.
The suspect with the knife is around 5ft 7in, aged in his mid-20s with short black hair and a moustache. He was wearing a black hoodie and had an English accent.
The third suspect is described as being about 5ft, of slim build, aged 40, bald, with a wrinkly face and a number of missing teeth.
He was wearing a black hoodie with a black jacket on top and has a Scottish accent.
Anyone with any information is asked to contact Police Scotland on 101, quoting incident number 3891 of October 2, or Crimestoppers anonymously on 0800 555 111.
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