The Okaz daily said the accused, who was not named, opened several Twitter accounts.
A special court for terrorism cases found him guilty of using the accounts to “call for protests and spread chaos to release detainees that are held for security and terrorism charges”.
He also joined a protest calling for the release of one detainee outside the prisoner’s home, it said.
Twitter is widely used in the conservative kingdom, which has repeatedly denounced bombings and shootings carried out in various countries by the Islamic State group and other extremists.
The kingdom itself has been targeted in attacks claimed by IS against minority Shiites and members of the security forces.
Last year the interior ministry said it had arrested hundreds of suspects involved in attacks and plots.
At the same time, the ideas of fundamentalist preacher Mohammed bin Abdul Wahhab, who co-founded the Saudi state, have been accused of fuelling deadly Sunni extremism around the world.
It is an offence for Saudis to travel abroad to fight, but they comprised the second largest nationality among “foreign terrorist fighters” with IS, according to a report last year by the inter-governmental Financial Action Task Force.
In a separate case, Okaz reported that the special court for terrorism sentenced a Saudi to 3.5 years in prison “for supporting Hezbollah” and possessing the flag of the Lebanese-based Shiite militant movement.
Alleged leaders of Hezbollah are under sanction by Saudi Arabia.