The petition set up by campaigning group 38 Degrees has attracted more than 44,000 signatures since Thursday (9 August).
"Dear Google. It's time for Google to pay its fair share of tax. There's nothing responsible about only paying £6 million in UK tax on hundreds of millions of pounds of revenue.
"Please do the right thing," the petition states.
However, Google has said that .
Google has based its international operations in the Irish Republic, where the corporation tax rate is 12.5 percent, compared to the main rate of corporation tax in the UK of 24 percent.