Scottish Green MSP Patrick Harvie wants the authorities at Holyrood to allow the use of social media during debates in the Scottish Parliament.
Harvie seeks to follow the example of Westminster where MPs have backed a motion allowing them to tweet during Commons debates.
In a report on the BBC TV Scotland News website, Harvie maintains that Twitter and Facebook could "open up" discussions to the electorate.
Any change to the current set-up at Holyrood would need to be brought forward by the Standards Committee.
Harvie has lodged a parliamentary motion on the issue which calls for an end to the ban on members "engaging the public through social media during debates".
It also urges the use of appropriate electronic resources to be allowed in the chamber.
Harvie told the BBC: "Holyrood has always been ahead of Westminster on public engagement, from the innovative petitions committee, to the decision to allow TV interviews in the building, a move which led the House of Commons to open up too.
"Now Westminster has set a lead on Twitter and social media while Holyrood looks stuck in the 20th century."
The MSP said the change could be "self-policing" and he warned "any MSP who tweets about the football while there is an important debate going on will quickly be found out".
He added: "Public confidence in politics is still at low ebb, and we should not be ruling out any constructive ways to engage people with the process.
"Twitter and Facebook can open up our discussions to the electorate, and we should have nothing to fear from that."
A Scottish Parliament spokeswoman said: "The Scottish Parliament's code of conduct currently states that MSPs must switch off electronic devices in the chamber."