Marc Hopkins, a constable at Northumbria Police, targeted three victims between November 2018 and December 2019 and sent "numerous" messages via text or on social media.
Newcastle Crown Court heard the women had contacted the force as victims or witnesses of crime and Hopkins used the details they provided to make contact.
The police constable, who has since resigned, was on duty and using a work device when he sent the messages .
A judge said Hopkins' behaviour was "revolting" and "undermines public confidence in all police officers".
Prosecutor Jolyon Perks told the court: "In respect of all three, the defendant initiated the text messages.
"The messages between the defendant and each complainant swiftly became sexually explicit.
"The sexual messages were sent from the defendant's work device and the sexual messages were sent while the defendant was on duty."
Mr Perks told the court Hopkins had been a police constable since 2013 and had started his career with Northumbria Police as a PCSO in 2009.
He resigned from his post in January 2020, after his offending was exposed.
Mr Perks told the court the first victim had contacted the police in November 2018 to report an assault on her friend during a night out.
She was taken to the police station and Hopkins took her statement.
The woman said Hopkins was "flirtatious and bantering" while he went through her account of the alleged offence.
Mr Perks added: "Shortly after, the defendant text her, using the number she had provided in the course of giving her statement, using his work phablet device, inquiring whether she got home safely, which began a messaging exchange.
"Thereafter, the content of the messages quickly turned sexual on the part of this defendant."
The court heard Hopkins tried to illicit sexual photographs from the woman.
The victim said she did not take the messages seriously at first and passed them off as "flirty banter" but she later said in a statement she found his behaviour "unacceptable".
She added: "It has put me off ringing Northumbria Police for anything.
"I go out of my way to avoid them in case one is Marc.
"The fact I have been contacted by an officer from Northumbria Police plays on my mind and I worry about him finding out where I live in case ofrepercussions."
The second woman contacted Northumbria Police in March 2019 to make a complaint of harassment against someone she had met on dating app Tinder.
Hopkins then used her details to send messages and sexual photographs of himself over Snapchat.
The woman said in a statement she had been on an "emotional rollercoaster" at the time and was vulnerable.
She said Hopkins had initially been "reassuring and supporting" when he took her statement but that quickly changed.
The woman said she believed Hopkins identified her "weaknesses" and branded him a "very sad individual".
The third woman had contacted the police after a run-in with a bouncer during a night out in December 2019.
Hopkins contacted her the following day and she confirmed she did not wish to take the matter further.
Mr Perks said: "However, messages from this defendant continued thereafter and again swiftly became sexual in nature."
The court heard Hopkins had accessed information on the Police National Computer about the woman, which highlighted how vulnerable she was, before he contacted her.
The woman said in a statement, despite her ordeal, she has not lost faith in Northumbria Police and has been grateful for how serious they took her complaint.
Judge Amanda Rippon sentenced Hopkins to three months behind bars.
The judge told him: "Your behaviour was a serious breach of public trust placed in police officers to behave professionally, responsibly, thoughtfully and nottake advantage of their position in relation to anyone that they meet.
"Your behaviour undermines public confidence an all police officers, it is a difficult enough job.
"Fortunately most police officers don't abuse that trust."
Ruby Shrimpton, defending, said Hopkins, who received commendations as an officer, "will never work as a police officer again" but managed to find newemployment.
Miss Shrimpton said Hopkins did not meet or attempt to meet any of the women and while the messages were "numerous", they occurred over short periods.
The court heard Hopkins wife left him and he went back to live with his parents after the offences.
Hopkins, of North Shields, admitted three charges of misconduct in public office.
The particulars of the offences are "while acting as a public officer, namely a Northumbria Police Officer, wilfully misconducted himself by sending messages of a sexual nature to (complainant), whose details you had obtained in your capacity as a Police Officer."
After the case, Superintendent Steve Ammari, Head of the Professional Standards Department at Northumbria Police, said: “We are aware of the case involving a former officer for which they have today been sentenced.
“After concerns were raised relating to his behaviour our Professional Standards Department began an investigation, managed by the Independent Office for Police Conduct.
“The officer was also suspended from duty and later resigned.
“The matter was further referred to the Crown Prosecution Service who subsequently charged him with three counts of misconduct in public office.
“We want to reassure the public that his actions are in no way representative of the officers and staff who every single day display the highest levels of professionalism and commitment to the communities we are proud to serve.
“We expect these standards to be maintained at all times and if anyone is found to have fallen below them we are committed to taking appropriate action."