Reform Scotland said its concept for “devolution plus” would make MSPs responsible for raising all the money it spends.
The group suggests transferring most welfare benefits while leaving responsibility for state pensions, sickness and maternity pay with Westminster.
Chairman Ben Thomson said £19.9 billion was spent on social protection in Scotland in 2009-10 – of which only £113 million was spent by the administration in Edinburgh.
The think-tank’s proposal would have seen the share increase to about £7.2 billion and Reform Scotland says shifting control of the budget in this way will be the only effective way for the Scottish Parliament to tackle poverty.
Mr Thomson said: “The reasoning behind this is to achieve a more coherent and effective approach to alleviating poverty.
“Many areas associated with this goal are already devolved to the Scottish Parliament, such as housing and social inclusion, yet the Scottish Government can make no concerted attempt to address poverty without the necessary tools and that requires welfare provision to be devolved.”
The suggestion is part of a submission to Holyrood’s inquiry into the Scotland Bill, which aims to increase the powers of parliament.
Reform Scotland said MSPs currently control 60% of public spending but are only responsible for less than 7% of funding.
The group said its proposal would remove the need for the block grant from Westminster, which the Scottish Government currently gets each year to spend.
Voters should be able to choose the approach as part of the SNP’s referendum, expected to be held towards the end of this five-year parliamentary term.
The intervention comes as MSPs on the Scotland Bill Committee continue to take further evidence from senior politicians, academics and experts.
The legislation aims to transfer more responsibility to Holyrood, including a wider £12 billion of financial powers.
Mr Thomson said there was an “imbalance” between Scotland’s responsibility for collecting income and its expenditure and Reform Scotland is now calling for income and corporation tax to be devolved.
A spokesman for Finance Secretary John Swinney said: “Support for independence is growing, and we are extremely confident of winning the case for independence and equality for Scotland in the referendum.
“There is also overwhelming backing for the Scottish Parliament having the full range of job-creating powers we need to boost jobs and recovery. It is clear that the provisions of the Scotland Bill in its current form fall far behind the ambitions of the people.”