Sen. Kirsten Gillibrand must come clean about her family’s connection to an alleged sex-slave cult upstate whose leader was arrested by the FBI on Monday, her Republican rival said.

GOP senatorial candidate Chele Farley noted that Gillibrand’s father, Doug Rutnik, was once a lobbyist for NXIVM and its founder, Keith Raniere.

“For Kirsten Gillibrand, the self-proclaimed #MeToo Senator, to claim ignorance about a notorious sex-slave cult, in her own backyard, is simply hard to believe,” said Farley.

Raniere hired Rutnik as a lobbyist in 2004, only to later sue him. Rutnik settled the case for $100,000.

A Gillibrand spokesman Tuesday referred The Post to a statement to Post columnist Richard Johnson last November, claiming she knew nothing.

“Senator Gillibrand had never heard of this group until she recently read about them in the newspaper,” said the spokesman, Glen Caplin.

He said the senator received a copy of a letter last fall about the group and referred it to the state attorney general to investigate. “She is glad that federal and state prosecutors have taken action in this case,” Caplin said.