Graffiti has been engraved into one of the stones at the Neolithic site near Stenness.
It is believed the stone was damaged sometime between Friday afternoon, April 5 and Sunday morning, April 7.
Officers are carrying out enquiries and are urging anyone with information to come forward.
Inspector David Hall said: “The stones at the Ring of Brodgar are priceless historical artefacts and the damage caused cannot simply be estimated in monetary terms.
“For someone to damage them in this way is a particularly mindless act.
“ I would urge anyone who has visited the area over the last weekend to think back and if they believe they may have seen something suspicious, even if it didn’t seem of much note at the time, to let us know.
“We would also would urge the public to continue to be vigilant at this site and report anything which could be of interest to police immediately.”
The ring was built around 2,500-2,000BC and covers an area of almost 8,500 square metres.
It is the third largest stone circle in the British Isles – behind Avebury and Stanton Drew – and is the largest in Scotland.
The Ring of Brodgar forms part of the Unesco Heart of Neolithic Orkney site which is considered a major prehistoric cultural landscape.
Information can be passed to Police Scotland by calling 101, quoting incident NK430/19, or call Crimestoppers on 0800 555 111.