The organisation is the leading militia in the north-eastern part of rebel-held Syria, and has taken control of parts of the civilian administration in the city of Raqqa.
It posted a new notice there this week saying it was open to receiving complaints from members of the public.
"Any one who might have a complaint against any element of the Islamic state, whether the Emir or an ordinary soldier, can come and submit their complaint in any headquarters building of the Islamic state," the notice said. "The complaint should be in writing, provide details and give evidence.
"We promise that we will ensure accountability for anyone committing violations, and they will be sent to the Sharia court of Iraq and al-Sham."
The Islamic State of Iraq and al-Sham - a popular term for Syria and Lebanon - is the name al-Qaeda has given to its new merged operation in the neighbouring countries.
The merger caused a split within the ranks of Jabhat al-Nusra, the Syrian organisation loyal to al-Qaeda which has led much of the recent fighting in the civil war on the rebel side. Parts opposed widening its mission outside Syria's borders.
Al-Qaeda has long had a reputation for bureaucracy, with papers rescued from the house where Osama bin Laden was killed by American special forces revealing the sometimes controlling nature of its correspondence with its various branches.
Earlier this week, a letter to Mokhtar Belmokhtar, the one-eyed guerrilla leader from North Africa, found by the Associated Press in a house in Timbuktu was revealed to contain stinging criticisms of him by the Shura Council of Al-Qaeda in the Maghreb for failing to submit his expenses, answer his phone regularly, or carry out attacks as instructed.
The notice in Raqqa may be a response to regular protests against aspects of its rule by civil society groups in Raqqa. On a recent visit, activists the Telegraph the group had tried and failed to ban smoking, a claim the group denies.
The notice was signed by the "Emir" of Raqqa, a title regularly claimed by Al-Qaeda sub-leaders.
Full literal translation:
Any one who might have a complaint against any element of the Islamic state, whether that be the Emir or a soldier, he shall come and submit his complaint in any headquarters of the Islamic state with the condition that this complaint shall be written and give details and evidence.
We promise you that we shall make accountable anyone committing violations and that person will be sent to the Sharia court of Iraq and al-Sham.
signed
Emir of Raqqa
Islamic state in Iraq and al-Sham
