A tour guide discovered the initials 'AA 2015' scratched into one of the stones while visiting the site.
Police Scotland and Historic Scotland have both been informed of the vandalism. It is believed it took place sometime between Monday and Thursday.
The Ring of Brodgar - the third largest stone circle in the British Isles - is regarded as one of Western Europe's most impressive prehistoric sites.
A spokesman for Historic Scotland said: "We were very disappointed to discover that the Rune Stone had been vandalised in this way and immediately contacted the police, as it is a criminal offence to damage a scheduled monument.
"Our conservation experts will review the damage soon and put together a programme of remedial work to mitigate the damage done.
"Fortunately incidents such as this are rare, and we continue to work with the local community to educate people on the significance of these prehistoric sites."
Orkney's neolithic Ring of Brodgar has been vandalised.