Reform Scotland said the temporary income tax rise should be introduced to pave the way for a social insurance model to pay for care.
It has produced a report titled The Cost of Caring, which also calls for a cross-party commission to tackle the issue of funding.
The think tank said the 1p rise can be used in the short term, but in the longer term it is unsustainable for a proportionately reducing workforce to pay for an ageing population.
Reform Scotland research director Alison Payne said: “Kate Forbes made it clear in her Budget that the Government is aware of the long term challenges in the social care sector.
“However, what is clear is that those challenges are cross-party and inter-generational.”
She continued: “When cool heads prevail in a constructive, cross-party environment, it will be clear that a move to a model of social insurance is both necessary and inevitable.
“It cannot happen overnight, which is why we propose a 1p increase in income tax to cover the immediate requirements, but work must now begin on the long-term solution.
“Doing this will be uncomfortable.
“But the consequence of not doing it will be far more so.”
Income Tax is the responsibility of the UK Government and is collected and managed by HMRC.
However, the Scotland Act 2012 gave the Scottish Parliament the power to set a different rate of Income Tax in Scotland, known as the Scottish Rate of Income Tax (SRIT). This took effect from April 6 2016.
Scotland Act 2016 extended these powers, enabling the Scottish Parliament to set the tax band thresholds (excluding the personal allowance) as well as the rates. This applies to all non-savings, non-dividend income of Scottish taxpayers, and took effect from April 6 2017.
Income Tax is not a devolved tax and HMRC continues to be responsible for the collection and management of Income Tax in Scotland, which includes the identification of Scottish taxpayers. The Scottish Income Tax collected by HMRC is paid to the Scottish Government.