Abhishek made the announcement at a rally organised by the Trinamool Youth Congress.
"BJP's Rahul Sinha's brother has joined the Trinamool today. Soon, his whole family will be with us," said Abhishek handing over a party flag to Sudip.
However, Mr Sinha claimed Sudip had been an active Trinamool worker for years and accused Abhishek of misleading the people by trying to show the BJP leader had a divided house.
"Much like I have been working for BJP, Sudip, my brother, has been an active Trinamool cadre for several years now. By handing him a Trinamool flag and announcing he has been inducted into Trinamool, Abhishek has mislead the people of Bengal," said Mr Sinha.
"This shows the Trinamool leadership is afraid of the rising might of the BJP and are trying petty tricks to show I have a divided house," he added.