The footage shows more than a dozen Scotland fans surrounding the statue and shouting away at the marble figure after the Scotland versus England game on Friday.
Two police officers are shown standing amongst the crowd as the boisterous crowd continued to chant at the English playwright.
The Tartan Army can be heard shouting: “You’re a sh*e Rabbie Burns, sh**e Rabbie Burns, oh you’re just a sh**e Rabbie Burns, sh**e Rabbie Burns” while pointing at the marble figure of the English poet.
The clip was posted onto Twitter by user @fc_1869 from Kilmarnock, East Ayrshire the following day.
The post was captioned: “Scotland fans singing ‘Yer just a sh**e Rabbie Burns’ to the William Shakespeare statue in Leicester Square. Best chant of the weekend IMO.”
The video has had over 330,000 views and hundreds of comments.
@C4mmy31 said: “Almost as funny as Paris in 98. The Tartan Army standing below the Eiffel Tower when the masses assembled burst into ‘it’s only a pylon’.”
@Muzzascot said: “My favourite Scotland chant is the one reserved for Italy games. ‘Deep fry yer pizzas, Wir gonna deep fry yer pizzas’.”
@oldbrickroad added: “I’m a scholar of English Renaissance literature and I say it’s f*****g hilarious.”
The marble figure, copied from Scheemakers’ 18th-century monument to Shakespeare in Poets’ Corner, Westminster Abbey.
It stands on a pedestal flanked by dolphins at the centre of a fountain.
Gerard Carruthers, professor of Scottish Literature at University of Glasgow, claimed in an academic article in 2016 that Burns was influenced by Shakespeare.
In an article titled ‘Haggis, neeps and soliloquies: the bonds that tie Robert Burns and Shakespeare’ he said: “As it turns out, the two countries’ national writers have a lot in common.
“Both men would likely have been surprised at their elevations to the status of iconic cultural figures.
Continuing: “William Shakespeare was a powerful influence on Robert Burns.
“If the latter exemplified certain Scottish literary and cultural traditions, he did so with Shakespeare in his DNA.”