Balwinder Singh, 54, attacked the girl in Edinburgh in 2016 then went on the run to Canada.
He was arrested in March this year and deported back to Scotland to face justice and is now facing a lengthy sentence.
Singh admitted raping the youngster during a brief appearance at the High Court in Edinburgh and was remanded in custody pending sentencing next month.
Following tha case, Detective Inspector Jonny Wright of Edinburgh's Public Protection Unit said: "Today, Singh has pled guilty to raping a 12-year-old child in 2016.
"My thoughts continue to remain with the victim and those impacted by Singh's actions.
"Singh fled the country soon after the offence came to light and travelled across the world seeking to avoid detection.
"However, his attempts would not be allowed to succeed and as a result of committed national and international partnership working, he was traced and deported from Canada, ultimately leading to his arrest in the UK on March 12."
Cops worked with their counterparts in Canada, as well as Scottish Police Authority Forensic Services, to secure a conviction.
He will be sentenced at a later date.
Det Ins Wright added: "Singh will now face justice for the abhorrent offence committed by him."