The arrest, on September 13, follows an internal report to South Yorkshire Police’s Professional Standards Department regarding concerns that the officer was having an inappropriate relationship with a female victim of crime.
The Police Constable, who was working in a response team, has been bailed until October 20 and is currently suspended from duties.
South Yorkshire police has not named the officer in its formal statement over the arrest.
Superintendent Delphine Waring, Head of Professional Standards, said: "We understand how concerning a report like this must be to our communities, particularly in light of recent national events and the need for forces across the country to be doing much more to transform toxic cultures and tackle abuse of women.
"This matter was brought to my department's attention by concerned colleagues and a full internal gross misconduct investigation was immediately launched alongside the criminal investigation.
"We are committed to being as open as possible about the professional standards of South Yorkshire Police and members of the public can be assured that any reports of this nature are dealt with swiftly and robustly."
It comes as police corruption and misuse of powers have been at the centre of national debate following the sentencing of former PC Wayne Couzens, who seven months used his position to abduct, rape and murder Sarah Everard.