Speaking at the Scottish Parliament on Thursday, Jackson Carlaw responded to suggestions a two-thirds majority should be needed in another vote.
At the last referendum held in 2014, Scots voted against independence by 55% to 45%.
After the issue was raised by SNP MSP Sandra White, Mr Carlaw said: "It is not the policy of the Scottish Conservatives to require a supermajority on any future referendum on any subject."
The Scottish Government's Constitutional Relations Secretary Mike Russell said he was "delighted" to hear Mr Carlaw outline that position.
He also criticised Scottish Tory MSP Murdo Fraser over a tweet sent on the fifth anniversary of the referendum last week, in which he wrote: "Leave/Remain and a two-thirds majority required. Bring it on", including a "wink face" emoji.
Mr Fraser responded: "What a sensitive soul the Cabinet Secretary is.
"He clearly can't take a light-hearted comment on Twitter with a wink emoji as anything other than that.
"But isn't it true that this Government is running scared of having a fair referendum, running scared of having the Electoral Commission decide on the terms of the question?
"We don't want another independence referendum, the people of Scotland don't want another independence referendum but we can't have the SNP gerrymander one if there is to be one."
Mr Russell said: "What the people of Scotland want is to move forward from the extraordinary Tory-created chaos of Brexit and the opportunity to do so exists if the people of Scotland choose their own constitutional future.
"Anyone who stands in the way of that isn't a democrat."
Scottish Greens co-leader Patrick Harvie said: "If a supermajority procedure had been in place for the last five years, there would have been neither a mandate for independence, nor for staying in the UK, neither for leaving or remaining in the European Union.
"Politics would be in even more of a mess than the Conservatives have managed to make of it."