The star of TV series The Apprentice posted a 24-line verse about Mr Corbyn on Twitter.
In the rhyme, the politician is criticised for Labour’s anti-Semitism row, his dress sense, his views on the monarchy and his reported previous relationship with shadow home secretary Diane Abbott.
The poem also mentions Mr Corbyn’s support for his local football club Arsenal and brands him the “worst Labour leader since records began”.
Alongside his “ode” to the Labour leader, Lord Sugar wrote: “Will some of the Labour MPs and Lords grow a pair and get him OUT.”
Last week, the peer deleted a tweet showing Mr Corbyn in a car next to Adolf Hitler after the post sparked a row.
Lord Sugar, who was born into a Jewish family, wrote alongside the image: “Many a true word spoken in jest Corbyn.”
The picture also added the caption: “When you’re pictured at Nuremberg and claim you thought you were going to a car rally.”
After Labour shadow chancellor John McDonnell led calls for him to delete the tweet, Lord Sugar apologised for sharing the image.
In response to Mr McDonnell, he added: “First let me say I am not the originator, it has been doing the rounds.
“You need to get Corbyn to make a firm statement about anti-Semitism. There is no smoke without fire in Labour.”
Between 1997 and 2015, Lord Sugar was a member of the Labour Party.
He was appointed to the House of Lords in 2009 when he became an “enterprise tsar” for Gordon Brown’s government.
The businessman, a former owner of Arsenal rivals Tottenham, quit Labour just days after the 2015 General Election, revealing he had been “losing confidence” in the party due to its “negative business policies” and “anti-enterprise” ideas.
Lord Sugar’s full poem about Mr Corbyn:
Jeremy Corbyn, a bit of a scruff
Asked what he could do to come over less rough
His fashion advisers worked on his new look
And a fifty quid Matalan suit’s all it took
Jeremy Corbyn, a stud of a man
A playboy was he with his lover Diane
She’d get into bed wearing only her blushed
And lie back with Jezza just thinking of Russia
Jeremy Corbyn, on Royals not keen
You won’t find him singing to God Save The Queen
No Cenotaph bowing for this bitter man
If elected he’d call for a monarchy ban
Jeremy Corbyn, says many a critic
Is a dangerous fool who is anti-Semitic
He often says “I’m not a Jew-hating man”
“I’m just a big Hamas and Hezbollah fan”
Jeremy Corbyn, an Arsenal man
Supporting the team with his Islington clan
He cheers the left winger when he goes along
And ‘Come on you Reds’ is his favourite song
Jeremy Corbyn, a yesterday man
The worst Labour leader since records began
Though his party is coughing and spluttering and dying
Old Jeremy Corbyn’s red flag is still flying