One of the people spearheading the campaign is Lib Dem MEP Caroline Voaden. She is asking the public to download the song using one of the online music stores.
As of Monday, the track entered the iTunes download chart in 24th position.
There are only five days left of the campaign with the track managing to become a bestseller on Amazon’s digital chart.
The next announcement of the chart will be this Friday – January 31 – the same day the UK will finally leave the EU.
The version the Remainers have chosen is one conducted by Andre Rieu and the Johann Strauss Orchestra.
The hope is that the campaign will create enough noise that major radio stations – such as Radio 1 – will have to air the track to their large audience.
Campaigner Andrew Tipler tweeted: “The Brexiteers can have their bells. We’ll have the airwaves.”
Ms Sturgeon has outlined plans of how Holyrood would remove application fees, salary threshold and employment sponsorship – all of which are required by the Home Office.
She said that an end to free movement from the EU would be “uniquely” damaging for Scotland’s economy as the country susceptible to population decline.
The Scottish First Minister said: “A common UK-wide approach to immigration simply hasn’t worked in Scotland’s interests for some time now.
“Brexit will undoubtedly exacerbate what was already a significant challenge.”
Ms Sturgeon has even spoke of her plans for having a Scottish visa.
This visa would use the existing Scottish tax code to tie the visas to employment specifically to the country.
British journalist Adam Boulton, however, said in an interview for Sky News that her proposal was “unlikely” to work as the visa allows freedom of movement in Britain and not only Scotland.
Ms Sturgeon said: “There is a proposal for a Scottish visa.
“So somebody who wants to come to the UK, as well as the other routes of application, could apply specifically to come work in Scotland.
“We would use the existing Scottish tax code to tie Scottish visas to employment here in Scotland.
“There are precedents for this kind of more regionalised approach to immigration in countries like Canada and Australia.
“It is a practical, workable solution designed to address specific Scottish challenges and I hope the UK Government will respond to it positively.”
Sky News host Mr Boulton replied: “It is unlikely isn’t it because if you had a Scottish visa you could come into Scotland and since we’re one country then move around the country freely. They might abuse it.”