The bird was spotted over the Aberdeenshire village of Craithe, close to the royal family’s Balmoral estate in the Cairngorms National Park.
Police have launched an investigation alongside the Royal Society for the Protection of Birds (RSPB) after the tourist who took the picture reported it.
The photograph shows the bird hovering with the trap clamped around its talons and a chain hanging from it.
The type of traps are regularly seen in the illegal trapping of birds of prey on grouse moors, which cover around 20 per cent of all land in Scotland.
RSPB Scotland’s Head of Investigations Ian Thomson told The Independent: “This picture of a golden eagle with a trap on its leg is sickening.
“There is no way a bird of prey could become caught in a legally set trap and as such it is absolutely clear this incident is a result of criminality.
“There have been a number of incidences where birds of prey have been caught in similar traps resulting in fatalities and we are concerned for the fate of this bird if it is not caught soon so it can receive veterinary treatment. We urge the public to report any sightings to the police.”
He added: “This kind of trap is used widely on grouse moors. Just a few years ago there was a case in the same area as this golden eagle has been spotted where a number were deployed illegally to target birds of prey.”
Police Scotland’s Sergeant Kim Wood said: “We would encourage anyone who has information which could help to locate this eagle to contact the police on 101.”
Grouse shooting is under increased focus as the season opened on 12 August and numerous naturalists and conservationists have called for an independent review into the impact of the practice.
A petition to ban driven grouse shooting – in which 500,000 grouse are shot dead a year – has reached 25,000 signatures.
The petition was created by BBC presenter and naturalist Chris Packham who told The Independent last month that in addition to illegal targeting protected species including birds of prey, gamekeepers on grouse estates legally target and kill “hundreds of thousands” of animals a year, including stoats, weasels, foxes and mountain hares in an effort to protect the grouse, which are then shot.
According to The Telegraph, the royal family’s annual summer grouse shoot was cancelled at Balmoral this year due to a shortage of birds, it said was due to “extreme weather and an outbreak of heather beetle,” which it said had impacted amounts of heather available for the grouse to consume.