A US special court martial held in Baghdad handed Sivits the maximum possible sentence of one year in prison on Wednesday.
Military officials gave their verdict after a three-and-a-half-hour trial.
Military judge Colonel James Pohl also sentenced Sivits, 24, to be reduced to the lowest rank of private, three grades below his present designation.
Sivits, 24, had earlier admitted to conspiracy to maltreat detainees, maltreatment of detainees and dereliction of duty around 8 November last year in the first trial over the abuse scandal.
He broke down in tears as he expressed remorse for taking pictures of naked Iraqi prisoners being humiliated.
"I'd like to apologise to the Iraqi people and those detainees," he said in his statement. "I should have protected those detainees, not taken the photos."
Wires were fastened to a
prisoner's hands and genitals
He also took responsibility for leading a detainee to a pile of inmates on the floor and then took a photograph of them while another guard, Specialist Charles Graner, kneeled on them.
Sivits said he was involved in a conspiracy to pile inmates on top of each other in a pyramid, but accepted only that someone had taken a photograph.
He also revealed that other US soldiers sexually humiliated naked Iraqi prisoners and punched one so hard he needed medical attention.
Sivits is the most lightly charged of the seven defendants ordered to stand trial so far, although he is also accused of manhandling detainees.
The now notorious photograph of naked Iraqi detainees forced to form a human pyramid of bodies and being sexually humiliated at Abu Ghraib prison in Baghdad has outraged the world.
Three other military prison guards were arraigned on more serious charges. Specialist Charles Graner, Staff Sergeant Ivan Frederick and Sergeant Javal Davis all declined to enter pleas at speedy procedural hearings in Baghdad on Wednesday.
There are worse pictures which
have not yet been released
The next hearings are set for 21 June.
The occupation and Bush administration, under heavy fire over the scandal, say the court martial is proof they are determined to punish anyone involved in abusing prisoners.
In sworn statements to army investigators leaked to the US press, Sivits had already indicated he will admit to the charges he faces in the hope of a more lenient sentence.
Additional photographs, described as worse than those released, have not been made public, feeding allegations the abuse was not just the work of rogue operators within the prison but went much higher up the military and political chain of command.
At least 13 soldiers have had courts martial in Iraq from May 2003 to January, according to an army list obtained by AFP, but none of those were open to the public.
New allegations of detainee mistreatment have emerged, notably from the Reuters news agency which said three of its Iraqi employees suffered physical and sexual abuse at the hands of US soldiers at a base near Falluja.
The employees informed Reuters immediately after their release in January, but only decided to go public after the US military said there was no evidence to back up the abuse charges, the agency said in a statement.