A Long Island woman’s unsubstantiated rape allegation after a drunken night in an upstate frat house has “destroyed” a New Jersey man’s life, he says in a $6 million lawsuit.

Catherine Reddington, 22, claims on social media that Alex Goldman, also 22, raped her vaginally and anally in a bedroom of Syracuse University’s Delta Kappa Epsilon fraternity following a party in April 2017.

She went to the police and the university with her accusations, and has posted her brutal tale of assault on Facebook in a campaign that Goldman says got him fired from his summer job and could get him tossed from his new college.

“I woke up in Delta Kappa Epsilon Fraternity in Alex Goldman’s bed confused, bloody, bruised, with ripped clothing and splinter[s],” Reddington wrote earlier this month. “Alex Goldman is a rapist.”

But Goldman — and the Onondaga County prosecutor — tell a different story of that night.

A months-long investigation, which included a medical exam, rape kit and bloodwork within 26 hours of the incident, found no evidence Reddington was assaulted, drugged or even had a sexual encounter with Goldman, according to court papers and the District Attorney.

The two engineering majors woke up fully clothed in Goldman’s bed, both claiming no memory of the night before.

Investigators found it “impossible to determine what, if anything, occurred that evening between Ms. Reddington and Mr. Goldman. There is no credible proof of any sexual conduct in this case, consensual or non-consensual,” an assistant district attorney wrote in a November 2017 letter, attached to Goldman’s lawsuit, explaining why Goldman was never charged.

Reddington slammed the DA’s letter on Facebook, calling it “disgusting.”

But Reddington’s accusations were enough to get Goldman booted from Syracuse in the fall, he claims. The school said it followed state and federal law in handling the complaint but declined to say why Goldman was expelled.

Now Reddington’s social-media posts targeting Goldman’s new school and employer show she’s out to “publicly tarnish his reputation and wreak havoc on his personal life and that of his family,” he says in his Brooklyn Federal Court defamation lawsuit.

Reddington posted Goldman’s picture, and links to his Facebook and LinkedIn profiles, in lengthy messages detailing the alleged assault, and accuses him of being a serial rapist. She added a #MeToo hashtag and linked to his current school, the New Jersey Institute of Technology.

“I write this post because this is not the first time Alex Goldman has raped someone and I want to make sure that it is the last,” she claims in a post earlier this month.

She also posted a screenshot of what appeared to be a message exchange with Goldman’s employer, Bohler Engineering, and crowed that he was fired.

“Due to the severity of the allegations and our zero tolerance policy, we have elected to immediately terminate the employment relationship,” the company replied in the screenshot posted on Reddington’s social media.

“Thank you to everyone for reposting and spreading the word on the monster that Alex Goldman is,” Reddington wrote alongside a post with a message from Bohler. “Thank you to Bohler Engineering for taking a stand against this disgusting excuse of a man.”

Bohler didn’t return a call for comment.

Onondaga District Attorney Bill Fitzpatrick said his office takes sexual assault cases seriously, but in this case, the evidence wasn’t there.

“What she has alleged about this office and this young man is simply not accurate,” Fitzpatrick told The Post. “I don’t know what her motivation is for that.”

Goldman chose to sue Reddington “because he could not sit idly by,” his lawyer Seth Zuckerman said. “Mr. Goldman will do everything possible to recover his good name.”

Reddington declined comment, calling it “a matter in the courts.”