The High Court in Glasgow heard that the girl became pregnant after being abused by Jason Middleton, from Grangemouth, who was looking after her. The girl, who cannot be named for legal reasons, decided to go ahead with the pregnancy.
The cour
t was told she is now trying to come to terms with having the child adopted.
Middleton, 19, admitted raping the girl on one occasion at a house in September 2005.
Prosecutor Jennifer Bain said: "This occurred while the accused was looking after the girl and they were alone together in a house.
"She gave birth to a daughter. She has tried to commit suicide on a number of occasions."
Ms Bain said that when Middleton was first questioned by police officers, he had denied having sexual contact with the girl.
However, the court heard that DNA samples were taken from the accused and the child, which confirmed that he was the father.
Solicitor advocate Richard Goddard, defending Middleton, said: "My client was deprived of a normal upbringing.
"He had no moral framework. He had almost non-existent parental guidance."
Temporary judge Rita Rae, QC, placed Middleton on the sex offenders register, but allowed him bail.
She deferred sentence until next month. The defence will make their plea in mitigation and a psychological report will be compiled on Middleton.
