The Ukraine Sponsorship Scheme, also known as Homes for Ukraine, allows citizens to volunteer to house refugees fleeing the war in Ukraine.
Sponsors offer accommodation for at least six months, with those receiving sponsorship allowed to live, work and study in the UK for up to three years.
But as of Monday, just 137 of these refugees had arrived in the UK.
Local authority figures cover refugees who have already been linked with a named sponsor prior to their arrival.
But around 5,600 of the 8,500 visas issued in Scotland fall under the Scottish Government’s “super sponsorship” scheme, where applicants do not have to be matched with a named sponsor at the point of application.
As of Monday, only 1,100 of those receiving "super sponsorship" had arrived in the UK.
The Refugee Council said it had received reports of delays at every stage of the application process, and of necessary documents not reaching refugees quick enough for them to travel.
Andy Hewett, head of advocacy at the charity, called the scheme "unfit for purpose".
A Home Office spokesperson called it "one of the fastest and biggest visa schemes in UK history" adding they are now “processing visas as fast as quickly as they come in” as a result of changes to the application system.