He was given an 18-month youth rehabilitation order at Havering Magistrates' Court in Essex after admitting burglary.
The boy, who cannot be named for legal reasons, stole a waste bin from Debenhams in Romford, Essex, on Aug 8 after the windows of the store were smashed by looters.
He is the youngest rioter in London to face prosecution, according to Scotland Yard.
He committed the offence just five days after being given a referral order for arson and criminal damage in an unrelated incident, the BBC reported.
Passing sentence, district judge John Woollard said, "You seem to think that nobody can stop the way you behave."
The Deputy Prime Minister, Nick Clegg, refused to be drawn on the case during a visit to Tottenham, saying, "the worst thing would be if politicians are second guessing the judges", but added "if you break the laws... you''ve got to face the consequences."
The boy, from Romford in Essex, took the waste bin, which was worth 50 pounds, after a group of males smashed windows at the store, causing 6,000 pounds of damage.
The boy was told that his local authority will dictate where he lives for the next six months.