Michael Fletcher, 31, of Blackwood Court, Bacup, Lancashire, admitted misconduct in a public office at an earlier hearing.
The court heard that he had sex twice with the woman at her Rochdale home after responding to a welfare call.
He was sentenced at Manchester Minshull Street Crown Court to 32 months.
The court was told that Fletcher first had sex with her while on duty on 21 July 2010, when he attended her house in Littleborough to make sure she was safe.
His duties in responding to a welfare call to a vulnerable adult were to contact social workers and ensure the woman was not in danger of being harmed.
He returned to her house later the same evening while off-duty and had sex with her again, the court heard.
'Abused position'Speaking after the sentence Chief Constable Peter Fahy said: "As soon as this was reported we took swift and decisive action, started an investigation and immediately suspended the officer from duty.
"Fletcher was sent to help this woman, ensure she was safe and arrange appropriate support from other agencies.
"Fletcher abused his position and disgracefully took advantage of the situation and such behaviour within Greater Manchester Police will not be tolerated.
"What this officer did has a huge impact on how the public view the police and the hard work and dedication of the majority of officers has now been undermined by his disgraceful and appalling behaviour."
"Because we dealt with this so robustly, the officer had no choice but to resign and due to the evidence presented before him he also pleaded guilty to the offences.
"No one is above the law, and officers who commit crimes will, quite rightly, be treated exactly the same way as everyone else."