A woman in the United States has been jailed after pleading guilty to having sex with the biological son she gave up for adoption and later tracked down on the internet.

Detroit area mother Aimee L Sword, 36, apologised at her sentencing on Monday in the Oakland County Circuit Court where she was sentenced to at least nine years in prison.

Jailed for sex with son ... Aimee L Sword, 36. Credit:AP

She had pleaded guilty to one count of first-degree criminal sexual conduct in a deal with prosecutors.

Police say Sword used Facebook in 2008 to find her son, who is now 16. She gave him up for adoption as an infant.