The District 49 Halls on Maxwell Road were sprayed with “IRA” over the weekend, sparking a police investigation.
The District Secretary with the Glasgow Southside Orange and Purple District condemned the vandalism as a “hate crime”.
He said: “The halls have been the subject of similar attacks over the years, luckily no one has been injured.
“The repeated nature is worrying, it feels targeted. The last attack was just six months ago.”
He added: “A supporter of the racist, sectarian and criminal gang known as the IRA spray painted the hall with its initials.”
Photographs reveal three places on the building that were painted.
A spokesperson for Police Scotland said: “On Monday, September 18, 2023, police received a report of a vandalism at the Orange Lodge in Maxwell Road, Glasgow.
“The incident is believed to have occurred sometime between Friday, September, 15, 2023 and Monday morning on September 18, 2023.
“Enquiries are ongoing.”
The Glasgow City Council graffiti removal service has been contacted by the Halls to remove the paint.