Glitter, whose real name is Paul Gadd, joined the social networking site on Thursday to announce an upcoming comeback tour.
The 67-year-old has had a string of legal problems after he was charged with child pornography offences in 1997.
"Announcing a tour? Some front u! I personally think boiling u alive is too good for u and ur sort," Barton tweeted.
"I am all for forgiveness for certain things but some things are unforgiveable."
Barton was imprisoned for six months in 2008 for common assault and affray over an alleged incident in Liverpool. The 29-year-old was released after 77 days.