The first tweet from Jayda Fransen, the deputy leader of Britain First, claims to show a Muslim migrant attacking a man on crutches.
This was followed by two more videos of people Ms Fransen claims to be Muslim.
Responding to Mr Trump’s posts, UK Prime Minister Theresa May’s official spokesman said it was “wrong for the president to have done this”.
Britain First was founded in 2011 by former members of the far-right British National Party (BNP).
The group has grabbed attention on social media with controversial posts about what they deem “the Islamification of the UK”.
It has put up members to run in European elections and by-elections on anti-immigration and anti-abortion policies, but has not secured any seats.
It also contested the most recent London mayoral election, receiving 1.2% of the vote.
The original video was shared by US conservative commentator Ann Coulter who Mr Trump follows.
Ms Fransen has more than 52,000 followers on Twitter.
She responded enthusiastically to Mr Trump sharing her tweets. She posted on her account: “Donald Trump himself has retweeted these videos and has around 44 million followers!”
“God bless you Trump! God bless America!” she added. The message was also shared on Britain First’s Twitter account.
Analysis by Anthony Zurcher, BBC News North America Reporter
Donald Trump is once again using Twitter to weigh in on contentious religious-tinged political issues in the UK.
In the past, he’s attacked London Mayor Sadiq Khan for mishandling a militant attack just hours after it occurred. He misattributed a rise in crime in England and Wales to the “spread of radical Islamic terror”. Now, he has retweeted a series of unverified videos posted by a far-right British nationalist group.
For the president, directing attention toward the UK seems to serve a domestic political purpose.
He cites events and opinions there as a warning to Americans of what could happen in the US if they do not heed his policy prescriptions on immigration and border security. The Muslim ban, the US-Mexico wall, increased deportations, the sharp reductions on refugee resettlement – it’s all part of the president’s “national security” package.
While most Americans probably haven’t heard of Britain First and are unfamiliar with European radical nationalist movements, there are white supremacist groups in the US that follow the actions of these overseas operations quite closely. The president on Wednesday signalled that he watches them too.
She will appear at Belfast Magistrates’ Court on Thursday 14 December.
Mr Trump’s decision to retweet the videos met dismay on social media.
Brendan Cox, whose wife, British MP Jo Cox, was murdered by a right-wing extremist who shouted “Britain First” before committing the act, has condemned the action.
TV presenter and journalist Piers Morgan, who has called himself a “friend” of the president, tweeted: “What the hell are you doing?”
“Please STOP this madness & undo your retweets,” he said.
The Council on American-Islamic Relations, a US-based civil rights group, said: “These are actions one would expect to see on virulent anti-Muslim hate sites, not on the Twitter feed of the president of the United States.”
“Trump’s posts amount to incitement to violence against American Muslims,” they added.
The head of the Anti-Defamation League (ADL), an anti-bigotry group, said the president’s retweets would “embolden bigots in the US and abroad”.
The Muslim Council for Britain called on the UK government to “distance” itself from the comments.
“This is the clearest endorsement yet from the US president of the far-right and their vile anti-Muslim propaganda,” a spokeswoman said.
Leader of the UK’s opposition Labour Party Jeremy Corbyn said Mr Trump’s actions posed “a threat to our society”.