The interview saw Baron Cohen disguised as an Israeli anti-terror expert chatting to Moore about a new paedophile detector he had developed.
Moore lost his Senate race in Republican-dominated Alabama to Democrat Doug Jones last December after being accused of sexual misconduct toward women when they were teenagers and he was in his 30s.
Moore, 71, whose wife Kayla is also a plaintiff, said he had been lured to Washington, D.C. on the pretense he would receive an award for his support of Israel, and would not have met Baron Cohen had he known what was planned. "During the segment, Defendant Cohen's "device" - as part of the false and fraudulent routine - purports to detect Judge Moore as a sex offender, thus defaming him".
A Showtime representative wrote in an email that they do not comment on pending litigation, and to their knowledge they had not been served with the complaint.
The lawsuit was filed in the Washington, D.C. federal court. When he uses it on Moore, the wand beeps.
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In July, Georgia lawmaker Jason Spencer, ridiculed for dropping his pants and using racial slurs on Who Is America?, said he would resign.
"I've been married for 33 years and never had an accusation of such things", Moore said.
However, he was instead interviewed by Cohen in character as Colonel Erran Morad, who waved a "paedophile detector" at him.
According to AAP and The Washington Post, the lawsuit was filed on Wednesday in the United States and accuses Cohen of smearing Moore's name and intentionally inflicting emotional distress. "If this is an instrument - and certainly I'm not a pedophile, OK?"
"Defendant Cohen and his agents including defendants Showtime and CBS knowingly made this false material representation to fraudulently induce Judge Moore to appear on the program, with Mrs. Moore present, where Defendant Cohen and defendants Showtime and CBS would falsely portray, mock and defame Judge Moore as a pedophile". He has denied the allegations.