Reform Scorland 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 and sickness and maternity pay with Westminster.
Chairman Ben Thomson said £19.9billion was spent on social protection in Scotland in 2009-10 – of which only £113million was spent by the administration in Edinburgh.
The think-tank’s proposal would have seen the share increase to about £7.2billion.
Mr Thomson said: ‘The reasoning behind this is to achieve a more coherent and effective approach to allieviating 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.’
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.