The Islamic State in Iraq and the Levant (ISIS) said it would give Christian residents "protection" if they agreed to the list of conditions.
The announcement came in a statement posted online.
Correspondents say ISIS is trying to implement an extreme interpretation of Islamic law in areas it controls.
Raqqa, seized by ISIS last year, was the first provincial capital to be completely in the hands of rebels.
'Risking the sword'
The directive from ISIS, citing the Islamic concept of "dhimma", requires Christians in the city to pay tax of around half an ounce (14g) of pure gold in exchange for their safety.
It says Christians must not make renovations to churches, display crosses or other religious symbols outside churches, ring church bells or pray in public.
Christians must not carry arms, and must follow other rules imposed by ISIS (also known as ISIL) on their daily lives.
The statement said the group had met Christian representatives and offered them three choices - they could convert to Islam, accept ISIS' conditions, or reject their control and risk being killed. » | Thursday, February 27, 2014