Hundreds are expected to arrive for the demonstration in Cheltenham, organised by the We Are Anonymous group.
They are supporting a legal challenge by civil liberty groups against the alleged use of mass surveillance programmes by UK intelligence services.
The UK government says interception is subject to strict controls.
Privacy International and Liberty are among those challenging the legality of alleged "interception, collection and use of communications" by agencies, at the tribunal.
This follows revelations by the former US intelligence analyst Edward Snowden about UK and US surveillance practices.
The case - also brought by Amnesty International, the American Civil Liberties Union and other groups - centres on the alleged use by UK intelligence and security agencies of a mass surveillance operation called Tempora.
The UK government has neither confirmed nor denied the existence of the operation.Investigatory Powers Tribunal Set up in October 2000 Can investigate claims against MI5, MI6 or GCHQ Eight men and two women make up the tribunal, which comprises senior barristers Members serve terms of five years after which they reapply or stand down Current president Mr Justice Burton has been on the tribunal since its inception
But documents leaked by whistleblower Mr Snowden and published in the Guardian newspaper claimed the existence of Tempora, which the paper said allowed access to the recordings of phone calls, the content of email messages and entries on Facebook.
The Investigatory Powers Tribunal (IPT) - which monitors whether the UK's spying laws are being observed - is seeking to determine whether the Tempora programme exists and, if so, whether it violates articles 8 and 10 of the European Convention on Human Rights.
It is also examining the UK's use of the US Prism mass data mining programme at a hearing in the Rolls Building in central London.
The BBC's legal affairs correspondent Clive Coleman said the "unprecedented legal challenge" - which will be held in public - was likely to be a "highly unusual hearing".
He said the case would be held on the basis of "agreed hypothetical facts".
A spokeswoman for Liberty, which campaigns for civil liberties, said it was making the challenge after concluding it was "highly likely" it had been monitored.
Lawyers acting for the security services will appear before the IPT to argue that, if indiscriminate mass surveillance had taken place, it was lawful and did not breach the right to privacy or freedom of expression.