One chicken was spotted in the grounds of their Hamilton-based centre on Wednesday, August 6, and a second was found the following day.
The birds have been nicknamed Mrs Tweedy and Bunty after characters from the film Chicken Run.
Centre manager Peter Fleming said, "At this stage we don't know where the chickens came from or how they got here.
"One of our staff members was taking a dog for a walk on Wednesday evening when she saw the first one.
"The second chicken was spotted the following day sitting on the window sill of our vet clinic.
"It's possible someone has dumped them but we haven't noticed any suspicious activity and the centre gates are locked when we close to the public.
"If anyone has information on how these chickens ended up here we'd ask them to get in touch as we would like to solve this mystery.
"For now, Mrs Tweedy and Bunty are quite comfortable in our care and we'll soon find them a nice new home."
Anyone who recognises the chickens should contact the Scottish SPCA's animal helpline on 03000 999 999.