Videos show the incident taking place at Kelvinhaugh Street in Scotstoun, but incidents have also been recorded between Earl Street and Dumbarton Road.
The GMB is raising concerns that the issue is getting worse again, with ten rats spotted at one time and staff not knowing where they are coming from.
Glasgow’s GMB convenor, Chris Mitchell, said: “Parts of Glasgow are worse than others. Earl Street in Scotstoun has been predominantly bad for years and just over the last couple of weeks it has been getting worse.
“Every week our workers go down to Scotstoun, they are citing reports and that video we took was taken at the student quarter on Kelvinhaugh Street just along from the Western depot.
“That area is really bad. There were about 10 rats at one point and they are being cited every week.
“We don’t know what’s happened or where the rats are coming from, the bins are getting emptied every week but there seems to be an influx in them.
“The residents in that area have already complained about it but it is a bad situation.
“This is a horrible situation and it’s not nice to see it. Workers expect it now but they don’t know where the rats are or where they are going to come from next.”
Asked about the recent incident, a spokesman for Glasgow City Council said: “Unfortunately our staff can encounter pests during the course of their work and we have well established procedures designed to protect staff health and safety.
“Most importantly if staff are concerned about an infestation they should report the incident to our public health team and they will look at an appropriate course of action.
“Thankfully no-one is harmed during this incident apart from an initial fright as the pests ran away.”
Rats have previously been spotted scurrying in and around bins at Bogmoore Road, Shieldhall in the South Side of the city as well as in the West End. Videos have also been shared online of rats munching rubbish out of overflowing bins in Govanhill.