Scotland's animal welfare charity was called to rescue the colourful conure on Monday evening after he was found on West Street.
The bird is now in the care of the charity's Glasgow Animal Rescue and Rehoming Centre, where he has been nicknamed Rio.
Animal Rescue Officer Amy Robb, said: "With his bright feathers, Rio would have been easy prey for wild birds so we're glad he was found before he came to any harm.
"He's obviously used to people as he jumped straight on to the man's hand and we think it's likely someone is missing him.
"Rio does have a ring on his leg but unfortunately we've not been able to use this to trace his owner.
"It's surprising how many stray birds arrive in our care, particularly during the summer months.
"They tend to escape when their owners are cleaning out their cages or letting them fly around a room. All it takes is for a door or window to be open and they're off.
"If no-one comes forward for Rio we'll soon find him a new home."
Anyone who recognises Rio is being asked to contact the Scottish SPCA's Glasgow centre on 03000 999 999.