Labour leader Mr Corbyn has declined a dinner invitation during Mr Trump's state visit to Britain later this year, having criticised him for "ripping up international treaties, backing climate change denial and using racist and misogynist rhetoric".
But Dudley North MP Mr Austin said Mr Corbyn was is no position to complain about spending time with Mr Trump, accusing the Labour leader of supporting "all sorts of extremists and in some cases terrorists and racists" during his time in politics.
Mr Austin quit the Labour party in protest over anti-Semitism and its lurch towards the hard left under Mr Corbyn's leadership.
"It's a shame he's not always been so choosy," Mr Austin said.
"He’s refusing to attend a dinner for the leader of our closest ally when he attended one for China’s President Xi – who leads a brutal dictatorship with no elections, human rights or free speech.
"He took thousands of pounds for presenting shows on the Iranian state TV channel, a country which executes people who disagree with the government regime, hangs gay men from cranes and imprisons British citizens.
"He travelled to Syria to speak to the brutal Syrian dictator Assad. According to Corbyn, the avowedly anti-Semitic terrorist organisations Hamas and Hezbollah are “friends” who should be invited to Parliament.
"He even laid a wreath at the graveside of the people who planned the butchery of Israeli athletes at the Munich Olympics.
"He calls Trump a racist but under Corbyn’s leadership, the Labour Party has become mired in anti-Semitism. Let’s not mince words: this is racism against Jewish people. Racism, pure and simple.
"I left the Labour Party because I think Jeremy Corbyn is unfit to lead the Labour Party and our country. And whatever you think of Donald Trump, Jeremy Corbyn has no right to condemn anyone else for extremism or racism."