Rishi Sunak was facing growing pressure over his Rwanda Bill on Monday night after two senior Tories confirmed they would defy him and join a rebellion against the legislation.
Mr Anderson, a popular figure on the Tory right, said in a post on X that he would back amendments to the Bill suggested by the veteran Tory Sir Bill Cash and former immigration minister Robert Jenrick, who resigned from Mr Sunak’s Government over the legislation.
Conservative former minister Brendan Clarke-Smith, who is also a deputy chairman, also said he would be supporting the amendments as "I want this legislation to be as strong as possible".
Asked whether he would keep his job, that he was given just seven weeks ago, by defying the PM he told reporters: "We'll see, it's not for me to decide."
Tory MPs will return to the House of Commons for a crunch vote on the Bill on Tuesday.
The amendments are seeking to disapply international law from the Bill and curtail asylum seekers' rights to appeal against flights to Kigali.
Mr Anderson and Mr Clarke-Smith join more than 60 MPs on the Tory right said to be considering abstaining or opposing the Bill.
Simon Clarke, a Tory MP and minister in Liz Truss' Government, told the News Agents podcast that he was “minded as things stand today to vote against” the Rwanda bill as he "did not believe it will work".
The amendments are unlikely to pass as they will be opposed by Labour. However, a third reading of the Bill is likely to pile intense pressure on Mr Sunak as Tory MPs could vote against the legislation inflicting damage to Mr Sunak's authority.
Mr Sunak introduced emergency legislation on his Rwanda plan last month after the Supreme Court ruled that the plan was unlawful.
Tory MPs from the centrist One Nation group have urged Mr Sunak not to accept right-wing amendments over fears it would breach international law.
One Nation chairman Damian Green said on Monday: “We've made our position clear that we, for all our reservations, we voted for the Bill at second reading. And we want the Government to carry it through unamended.”
Hitting back at right-wing colleagues, ex-Justice Secretary Sir Robert Buckland warned that toughening up the Bill will "cause problems".
Sir Robert said: "I think in a nutshell, the Government would be best advised not to accept any of the amendments from my colleagues on the right, because the Bill then will cause a problem for us here. So we're hoping that common sense will prevail."The Rwandan Government has also insisted that it will pull out of the agreement if it does not comply with international law.
The Prime Minister on Monday sought to downplay suggestions of infighting between Conservative factions, insisting he was “talking to all my colleagues” about the future of the Bill.
He said there are circumstances under which he would also be prepared to ignore injunctions from Strasbourg - so-called Rule 39 orders - blocking flights from taking off to the east African nation.
“I know everyone is frustrated - I'm frustrated about the situation - and they want to see an end to the legal merry-go-round," he told reporters during a visit to Essex.
“I'm confident that the Bill we have got is the toughest that anyone has ever seen and it will resolve this issue once and for all.”
On the eve of the Commons showdown, Tory political strategist Isaac Levido warned the 1922 committee of backbenchers: "Let me be clear. Divided parties fail."
The vote comes as fresh polling suggested that the Tories could be on course for a 1997-style wipeout at the next general election.
A YouGov survey of 14,000 people indicates that the Conservatives could hold on to as few as 169 seats as Sir Keir Starmer's Labour enters Downing Street with 385.
The same survey showed that 42 per cent of voting-age adults believe people who cross the Channel in small boats should be immediately removed with no right of appeal, the Telegraph reported.
Six in ten voters believe the Rwanda Bill will not reduce the number of Channel crossings in its current form, according to the poll.