The think-tank said the Home Office would be "beyond hypocrisy" if it allowed Dr Ibrahim Moussawi into Britain just weeks after barring Geert Wilders, the Dutch politician, because of his alleged anti-Muslim views.
Dr Moussawi is a spokesman for the Lebanese-based militant group Hizbollah, the military arm of which is banned in Britain as a terrorist organisation.
He has allegedly called Jews "a lesion on the forehead of history" and said of Israel: "Pain is the only language that the enemy understands."
Douglas Murray, director of the CSC, has written to Jacqui Smith, the Home Secretary, warning her that he will instruct lawyers to seek an arrest warrant for Dr Moussawi if he is allowed into the country.
The think-tank has already sought advice from barrister Paul Diamond, an expert in religious affairs law, on using war crimes legislation and a legal precedent from 2004 to seek, independently, an arrest warrant from a magistrate.
Mr Murray said: "This is the deepest hypocrisy, in fact, it is worse than hypocrisy on behalf of the British government.
"The government clearly do not have a grip on this. Britain is still a place where terrorists and terrorist supporters can come to incite and recruit."
Dr Moussawi is due to address a conference at the University of London's School of Oriental and African Studies, on March 25, on the subject of political Islam.
Senior civil servants and police officers are among those who will pay up to £1,890 to attend the event, which is intended to improve understanding of radicalism.
Dr Moussawi has been granted a visa to visit Britain at least twice in the last two years but it is understood that he has yet to apply for permission to re-enter.
He was banned from visiting Ireland in 2007. On previous visits to the UK he has spoken at events organised by the Stop The War Coalition, and has been billed as a Hizbollah spokesman.
Apart from his role as a public face of the militant group, Dr Moussawi edits a weekly Hizbollah newspaper and was the political editor of a Hizbollah television station which is banned in the US, France and Spain because its output is seen as anti-Semitic.
In its letter to Ms Smith, the Centre for Social Cohesion said: "We would be grateful for a full answer as to why this policy is not being applied to Dr Moussawi in the light of recent exclusions of other non-nationals seeking to enter the United Kingdom.
"It is the position of the Home Office that individuals are banned from entry in the United Kingdom if 'they stir up tension and provoke violence to others'.
"Dr Moussawi would threaten community harmony and clearly breach this condition. If Dr Moussawi arrives in the UK we will instruct counsel to seek a warrant for his arrest."
In 2004, Bow Street magistrates' court considered an application for an arrest warrant for General Shaul Mofaz, then the Israeli defence minister, at the request of Palestinian groups.
The warrant was not granted, on the grounds that the minister would enjoy state immunity.
Any prosecution which would arise from such an arrest warrant would have to be authorised by the Attorney General.
Mr Wilders, 45, planned to show his controversial film which links the Koran to terrorism, but was banned from entering Britain because he was classed as someone likely to incite hatred and threaten "community harmony".
The politician had been invited by a peer to show his 17-minute documentary, entitled Fitna, and hold a question-and-answer session in Parliament.
He has urged the Dutch government to ban the Koran and has warned of a "tsunami" of Islam swamping the Netherlands.
After being turned back at Heathrow airport, Mr Wilders described the UK government as the "biggest bunch of cowards in Europe" and criticised them for barring a democratically-elected politician from a fellow European Union country.
The Conservatives have urged the Home Secretary to bar Dr Moussawi.