He has more than 70,000 Twitter followers and frequently mocks IS. Twitter has made no comment.
Twitter recently updated its rules on "abusive behaviour and hateful conduct" in a bid to better protect users. It has been criticised for not doing enough to stop IS using the platform for propaganda purposes. The company says users are not allowed to threaten or promote terrorism.
Mr El Baghdadi told the BBC he received a message from Twitter saying he had "violated" its rules but not specifying the offence. He has accused Twitter of being racist.
"I don`t think a single Arab country exists that doesn`t have a family with the surname El-Baghdadi," he tweeted.
The activist, who also researches radicalisation, said the alleged incident raised questions about Twitter`s security processes. He said the company needed to be "more transparent" about why and how people are suspended.
Twitter should "engage power users who deal with trolls regularly", he added. The company does not comment on individual users` cases for privacy reasons.
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