The small group was seen at the landmark in a Facebook Live video on Tuesday afternoon, with Police Scotland confirming officers were still in attendance hours later.
In the 13-minute video, a woman says the castle “belongs to the people” and that they are “taking our power back”.
She adds the Scottish people have been “lied to all our lives” and that the “building belongs to us, we have taken the castle back” in an effort to “restore the rule of law”.
Another man then says: “Treason’s been going on for that long now, we can’t sit back and let everybody perish under the stupid legislation and fraudulent government tyranny, so let’s just take it all back, not just the castle.”
The woman then speaks again calling for “no more enslavement” and the “people and commonwealth are going to be free”.
She tells viewers they are going to “take everybody down”, including government, the courts and “the crown is coming down today”.
After saying the group is “putting we, the people, back into power”, a second man adds: “We are the people.”
The woman also claims “corrupt, evil, satanic paedophiles are running this country” and Scots have been kept “like peasants for 800 years”.
As police appear, she shouts “notice to compel” and informs officers they are seizing the castle under article 61 of Magna Carta – “the only law in the land” – which predates the Act of Union.
The woman says she has put Police Scotland Chief Constable Iain Livingstone “on notice” about them taking the castle.
One officer asks the woman for her name, to which she says she is “not obliged” to do, before identifying herself anyway.
The police constable then asks: “How many more people are you expecting to come to Edinburgh Castle today to join your protest?”
When she tells him “it’s not a protest, we’re actually taking it back” he replies: “Right, no worries.”
A Police Scotland spokesman said: “Officers are currently in attendance at Edinburgh Castle and are engaging with a group of people who have gathered within the castle grounds.”