While it was not immediately possible to verify the accounts published by various Twitter feeds, "Jihad News" said the alleged thief, in the north Syrian town of Maskanah, had confessed to his crimes and requested the form of punishment according to strict traditional religious codes.
The account claimed he had "asked that his hand be cut off to cleanse his sins".
The punishment was carried out by an al-Qa'ida-affiliated group known as Isis, or the Islamic State in Iraq and the Levant.
Mainly composed of fighters from outside of Syria, Isis is widely regarded as the most radical Islamist rebel group fighting against the forces of President Bashar al-Assad.
Isis controls much of rebel-held areas in the north of the country. In the city of Raqqa, it has demanded that Christians pay a levy in gold and curb displays of their faith in return for protection.
It has also reportedly banned Christians from owning weapons and from selling pork or wine to Muslims or drinking wine in public.
- UK Independent