Police have arrested a 59-year-old man over allegations of "malicious communication" via email and Twitter to Tory MP Louise Mensch, Scotland Yard said on Monday.
In a statement, police said Frank Zimmerman had been charged after being arrested on 25 August.
Zimmerman had been on police bail, pending further enquiries, before being charged.
Mensch had claimed in August that "morons" had threatened her children by email.
She tweeted saying that she had passed the incident on to the police, adding: "I don't bully easily, kids. Or in fact at all."