Mr Agrawal, who has courted controversies in the past too over his statements, made the remarks in the presence of BJP leaders, including Union minister Piyush Goyal, at a press conference held at the party headquarters here to announce his joining the BJP.
"I have been compared with those who dance and work in films," Mr Agrawal said, leaving the BJP leaders on the dais squirming.
BJP spokesperson Sambit Patra, however, immediately distanced his party from Mr Agrawal's remarks, saying his party respects people from all fields and welcomed them in politics.
Mr Agrawal also expressed his affection for SP patriarch Mulayam Singh Yadav and his cousin Ram Gopal Yadav, but said the party's strength in Uttar Pradesh has depleted.
He also praised Prime Minister Narendra Modi and party chief Amit Shah and claimed that the people of his community were solidly behind the saffron party.
Mr Agrawal also said that his MLA son will vote in favour of the BJP in the Rajya Sabha polls.
Mr Agrawal's term as Rajya Sabha member is ending on April 2. Bachchan has once again been nominated to the upper house by the Samajwadi Party.
His remarks in the House mocking Hindu gods had sparked an uproar last year.