The video is part of BrewDog's Equity For Punks crowdfunding programme, encouraging people to invest in the business.
In the video, the BrewDog founders say they will "do anything" to attract investment, but say "don’t make us do this" whilst pretending to be homeless people, then dressing in women’s underwear and pretending to be sex workers. One of the founders then says: "I’d do it, but I’d need a bath afterwards."
The petition has been launched by Care2, an online campaigning group, urging BrewDog to pull the campaign, apologise and donate money to charities working for the rights of homeless people, trans women and sex workers.
James Watt, co-founder of BrewDog said: "The video we created was to launch the CrowdCube aspect of Equity for Punks and was made in the spirit of fun and sending ourselves up – it’s a shame that some people have taken offence where none was intended. We have a history of supporting and championing the LGBT community, and will continue doing so. Watch this space."
Care2 campaigner and petition author Beth Granter said: "The response from Brewdog is disappointing and misses the point. They are clearly mocking marginalised groups of people and that's just bad business. BrewDog's campaign is at the very least feeding into transphobic and anti-sex worker attitudes. Intent is not the point. Plain and simple - BrewDog's campaign is offensive and insulting to trans women and sex workers - and BrewDog needs to apologise and pull the video now."
The public's response to the video on YouTube has been mixed; one viewer described it as "Discriminative and boring" while another said "Im confused... There is nothing that they say or do that in any way suggests that they are trying to be trans at all."
In the past BrewDog has created products in support of the LGBT community - the company released a "protest beer" mocking Russian president Vladimir Putin’s homophobic laws.
Last month BrewDog switched its PR account from Manifest to The Romans. The video was created before the new appointment.