It comes amid global outrage at a ban on people arriving in the United States from seven Muslim-majority countries was imposed by the President on Friday in an executive order.
The UK Government is compelled to respond to all petitions that received more than 10,000 signatures and if a petition reaches 100,000, it must be considered for a debate in Westminster Hall.
But Downing Street has already stressed its position had not changed on the US President’s trip. “An invitation has been extended and accepted,” a Number 10 spokesman added. According to the BBC another source suggested rejecting Mr Trump would be a “populist gesture”.
Citing Mr Trump’s “well documented misogyny and vulgarity”, the petition calls for Mr Trump to be allowed into the country, but not invited to meet the Queen.
“Donald Trump should be allowed to enter the UK in his capacity as head of the US Government,” the petition reads, “but he should not be invited to make an official State Visit because it would cause embarrassment to Her Majesty the Queen.”
It continues: “Donald Trump’s well documented misogyny and vulgarity disqualifies him from being received by Her Majesty the Queen or the Prince of Wales. Therefore during the term of his presidency Donald Trump should not be invited to the United Kingdom for an official State Visit.”
The petition comes in response to Mr Trump’s temporary ban on those travelling to the US from a group of predominately Muslim countries – Iraq, Iran, Libya, Somalia, Sudan, Syria and Yemen.
On Sunday the Foreign Secretary Boris Johnson, who faces being hauled before MPs later on Monday, clarified the US policy, claiming that most UK citizens will not be affected by Mr Trump’s ban after it emerged it would affect dual national citizens.
The Foreign Office said Britons with dual citizenship would be exempt from the controversial travel ban, but UK residents have been caught up in the chaos.
The US president accepted an invitation to visit Britain later this year, where he is due to be hosted by the Queen and would be treated to all the pomp and ceremony accorded to a state visit.
Thousands have protested in cities across the country, with major demonstrations planned in Britain on Monday.
Baroness Sayeedi Warsi, a former Conservative Cabinet minister, indicated the President should not be given the honour of a state visit. "We have to question whether, in Britain, this is something that Britain should be doing for a man who has no respect for women, disdain for minorities, little value for LGBT communities, no compassion for the vulnerable and whose policies are rooted in divisive rhetoric," the Tory peer said.
She added: "Those who run and govern this country bowing down to a man who holds the views that he holds, values which are not the same as British values, I think is sending out a very wrong signal."
Lady Warsi told the BBC Radio 4 Today programme that politics is facing a "crossroads" following Mr Trump's election.
"If we want to continue to be a country that supports liberal, progressive values in which all have equal worth and equal value in our society, then we have to be clear that we voice that view and that opinion, so that people in this country know that whatever crazy things the President of the United States may be doing, it is not what we believe and not what we support."
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies