Paphos police on Tuesday said they are investigating the second rape claim in less than a week.
A 37-year-old woman reported she was raped by a 45-year-old man on July 24, police said.
An arrest warrant was issued against the man after the woman filed a complaint to the police on Monday.
Media reports said the 45-year-old man is the former partner of the woman and had invited her to his house, where he got her drunk and proceeded to have sex with her against her will.
Investigations into the case are ongoing, police said.
This is the second rape claim reported in Paphos in the last five days.
On Friday, a 21-year-old woman also reported she was raped by an unknown man in the coastal area in Paphos.