Pc James Ankrett pleaded guilty to a charge of "corrupt or other improper exercise of police powers" at Wolverhampton Crown Court on Tuesday after he formed an inappropriate relationship with the woman in July 2017.
The officer, from Hednesford, was charged in 2019 following an investigation by the Independent Office for Police Conduct.
A force response officer, Pc Ankrett was restricted from duties and has been working in a non-public facing role since the allegation was made.
He is now being suspended from duties and will be sentenced at Wolverhampton Crown Court in October.
Deputy Chief Constable Vanessa Jardine said: “The actions of PC Ankrett have undermined the very essence of our force’s core value of protecting the public and helping those in need.
“He used his position to conduct a wholly inappropriate relationship and has significantly damaged the reputation of the force.
“He will now face an internal disciplinary process.”