Former PC Gavin Donaldson, from Midlothian, had admitted telling the woman to delete thousands of emails and messages they had exchanged which were evidence of their relationship.
He further told her not to hand over her phone to anti-corruption officers who were investigating his behaviour and tried to influence what she would say to them.
At a hearing last month, the former officer pled guilty to a charge of attempting to pervert the course of justice.
Edinburgh Sheriff Court heard that Donaldson, 45, who was based at Dalkeith Police Station, met the woman when she was a teenage victim of serious crime.
Despite being aware of her vulnerabilities, he cultivated a relationship with her which lasted until November 2020 when he was suspended from duty.
Returning to Edinburgh Sheriff Court for sentence today (27 Apr), Donaldson was sentenced to 14 months imprisonment.
Justin Farrell, who heads the Crown’s specialist Criminal Allegations Against the Police Division, said:
“Gavin Donaldson abused his respected position as a police officer.
“A woman who trusted him to provide professional help and support found herself being manipulated by him and encouraged to cover-up his entirely inappropriate behaviour.
“I commend this woman’s bravery in speaking out about Donaldson’s actions.
“Members of the public will be protected by the law.
“They should have confidence that prosecutors will respond robustly and independently to reports of criminal behaviour by police officers.”