His CIA jailers held the handgun and drill close to the prisoner to frighten him into giving up information.
Al-Nashiri, who US investigators believe is connected to the bombing of the US Navy destroyer Cole in 2000, was also subjected to a form of simulated drowning known as waterboarding, The Washington Post said.
The report, completed in 2004 by John Helgerson, the inspector-general, also says that a mock execution was staged in a room next to one suspect.
CIA officers fired a gun in the next room, leading the prisoner to believe that a second detainee had been killed, The New York Times said.
Details of the report were first published by Newsweek magazine on its website late on Friday.
A federal judge in New York has ordered a redacted version of the classified CIA report to be made public on Monday, in response to a lawsuit by the American Civil Liberties Union.
Lawyers for the justice department and the CIA have been scrutinising the long-concealed agency report since June to determine how much of it can be made public.
Al-Nashri was one of two CIA detainees whose interrogation sessions were videotaped, but the tapes were destroyed by CIA officers in 2005, the Times said.