Police said the girl, now 15, was left so traumatised by the "horrifying ordeal" that she only came forward to report it last month.
It happened in the city's Drumchapel area on Thursday, December 15, 2011.
Officers said the girl was raped in an alleyway, near to the Donald Dewar Sports Centre, as she walked towards Southdeen Park from a friend's house in Cloan Avenue.
The man, who is believed to be in his 40s, approached her on a bridge nearby and engaged her in conversation, before pushing her into the alleyway.
He then forced her to the ground and raped her.
Detectives believe a distinctive tattoo on the rapist's right thigh, depicting a ship's steering wheel, may be key to tracking him down.
Officers also said he was wearing an Armani stud earring in his left ear.
Detective Inspector Dougie McKinlay, who is leading the inquiry, told the Evening Times: "We will deal with this investigation the exact same way we would if the incident was reported today.
"Officers have carried out detailed searches of the area and we are looking to obtain any CCTV for the surrounding area.
"I believe that the description of this man, including his distinctive tattoo and earring, will be key to identifying him.
"Someone out there must recognise the description and realise that they know who this man is.
"I would urge them to contact police.
"It is vital that we identify and trace this man as soon as possible."
A dedicated team of detectives has been carrying out extensive inquiries into the attack, which took place between 8pm and 9.30pm.
Police said the rapist was white, between 40 and 50 years old, of stocky build, with short dark brown hair.
He was wearing a grey jogging suit and a red 'Puffa' jacket.
Detective Inspector McKinlay, who is based at Glasgow City Centre and West CID, added: "Some time has passed since the crime took place and we are relying on witnesses to come forward.
"I am asking people to think back, check their diaries.
" Would you have been in that area then?
"Do you go to or did you attend the Donald Dewar gym around that time?
"Do you recognise the description of the suspect?
"Did you see a man fitting that description around the areas of Cloan Avenue, Garscadden Road or Southdeen Park?
"Any detail or information which you may remember could be vital in this investigation and I would appeal for people to get in touch with us."
Strathclyde Police said the young girl was now being given the support she needs.
Anyone with any information is asked to contact Drumchapel CID on 0141 5323600.