Stephen Gethins says an independence referendum "has to be on the cards"
A spokesman for the Scottish National Party says a vote for Scotland to remain in the EU is "the right thing to do."
It comes following the surprise result which will see the United Kingdom leave the bloc.
Stephen Gethins told the Moncrieff Show here on Newstalk: "Scotland voted overwhelmingly in favour of Remain...so if we're having a debate about democracy, Scots have voted to Remain."
"I think that us having the opportunity to remain within the European Union is a sensible thing to do - and would be the right thing to do in these circumstances."
This follows comments from SNP leader Nicola Sturgeon, who said that a second referendum on Scottish independence is "highly likely."
"Scotland does now face that prospect - it is a significant and material change in circumstances - and it is therefore a statement of the obvious that the option of a second referendum must be on the table. And it is on the table", Ms Sturgeon said
Mr Gethins also said that Scotland "There has been a material change in circumstances in that union (of the UK) today, which is that Scotland has been taken out of the European Union against its will."
"And given that material change of circumstances, an independence referendum has to be on the cards."
Asked if there was a legal case to be answered on the issue, Mr Gethins replied: "I think it's more the democratic case (which is) the stronger one."
"Remember the EU is a club for independent member states, the United Kingdom isn't - that's why Ireland's a member (of the EU) and it's not a member of the United Kingdom."
"Hopefully the UK government will recognise that democratic will of the people of Scotland, that we can protect our status to the EU as we voted for", he added.