Lee Martin-Cramp, 26, used his job as a constable in the Metropolitan Police to dupe the victim into trusting him.
He was dismissed by Scotland Yard last month after being convicted of rape by Antigua and Barbuda’s High Court in May.
Martin-Cramp, who had been posted to Wimbledon police station before his arrest, met the victim via dating app Tinder while visiting the island for a friend’s wedding in May 2015.
The woman, reportedly a devout Christian, had told him before they met that she would not have sex with him, according to local media.
After a date in a bar, they went back to the woman’s apartment to share a bottle of wine and watch a film. Martin-Cramp is said to have spiked the victim’s drink when she left the room to get changed.
He raped her after she complained of feeling dizzy.
Martin-Cramp was arrested over the attack by the Met’s Extradition Unit in June 2016.
His extradition in September last year was the first time a UK citizen has been handed over to Antigua to face criminal charges.
He was sentenced on Thursday at Antigua’s High Court.
According to the Antigua Observer, he will spend his jail term at a former US naval base on the island rather than the overcrowded state prison, in the capital St John’s, which has been criticised by human rights groups.
Commander Catherine Roper, of the Met’s Directorate of Professional Standards, said: “Former PC Martin-Cramp has been sentenced for an extremely serious offence.
“The evidence given during the trial included distressing details of how the victim trusted him because he was a police officer, and how he took advantage of that trust in the most deplorable way.
“The officer’s actions fell well below that of any decent person, but particularly a person whose job is to protect people and keep them safe.”