The Syrian Observatory for Human Rights said the youngest of the 12,751 victims was just 12 years old.
"Some of the families of those killed under torture were forced to sign statements that their loved ones had been killed by rebel groups," said Observatory head Rami Abdel Rahman.
He told AFP the toll did not include more than 20,000 detainees who have "disappeared" in government prisons and whose fate remains unknown.
The most notorious detention centres include those operated by Syria's Air Force Intelligence and Military Intelligence services.
In total, the Britain-based Observatory said an estimated 200,000 people have been arrested over the past four years.
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Security officials starve detainees to death, deny medicine to sick prisoners and subject them to psychological torture, Abdel Rahman said.
He said those arrested include political activists, rebels and regular demonstrators.
Former detainees have described the horror of the torture techniques, many of which have become infamous throughout Syria.
According to a 2013 Human Rights Watch report, Syrian security officials beat prisoners with batons and metal rods as they hung from the ceiling by their wrists.
A report issued by 21 international aid organisations on Thursday said rape and sexual abuse were also used in regime detention centres as a "method of war."
More than 210,000 people have been killed in Syria since the uprising began, according to the Observatory.