Donald Trump was sworn in for a historic second term as US president on Monday, pledging a blitz of immediate orders on immigration and the US culture wars as he caps his extraordinary comeback.

With one hand raised in the air and the other on a Bible given to him by his mother, the 47th US president solemnly took the oath of office beneath the huge Rotunda of the US Capitol.

Republican Trump and outgoing Democratic President Joe Biden had earlier travelled by motorcade together to the Capitol, where the ceremony was being held indoors - and with a much smaller crowd - for the first time in decades due to frigid weather.

Earlier, they and their spouses met for a traditional tea at the White House.

"Welcome home," Biden said to Trump as he and First Lady Jill Biden greeted their successors at the front door to the presidential residence.

Trump, 78, was a political outsider at his first inauguration in 2017 as the 45th president, but this time around he is surrounded by America's wealthy and powerful.

The world's richest man, Elon Musk, Meta boss Mark Zuckerberg, Amazon chief Jeff Bezos and Google CEO Sundar Pichai all had prime seats in the Capitol alongside Trump's family and cabinet members.

Musk, who bankrolled Trump's election campaign to the tune of a quarter of a billion dollars and promotes far-right policies on the X social network, will lead a cost-cutting drive in the new administration.

While Trump refused to attend Biden's 2021 inauguration after falsely claiming electoral fraud by the Democrat, this time Biden has been keen to restore the sense of tradition.

Biden joined former presidents Barack Obama, George W. Bush and Bill Clinton at the Capitol. Former first ladies Hillary Clinton and Laura Bush were there but ex-first lady Michelle Obama pointedly stayed away. (AFP)