Delegates at the party’s autumn conference in Glasgow voted overwhelmingly for a motion calling for the repeal of the Sovereign Grant Act 2011.
The party argued that ordinary people were being “shafted by a rich elite” under the current system and the money would be better spent on social care.
The SNP’s political education convener Julie Hepburn said the endowment was “basically the equivalent of the Royal Family winning the Lottery every single year”.
“No need for the Queen to play Euromillions,” she said. “With the Sovereign Grant, Her Majesty is purring all the way to the bank.”
The Sovereign Grant Act pays the royal household a proportion of profits from the Crown Estate, which has some £272m worth of assets in Scotland.
The Royal Family has seen its income increase substantially since the introduction of the Act, rising from £31m in 2012/13 to more than £76m this year.
“This is our money — money that could otherwise be spent on the public good,” Ms Hepburn said. “Under the Sovereign Grant system there is no accountability for the size of the payments that go to the royal household or any limitations to ensure proportionality.
“If profits double, the payments double. At a time when the UK Government is insisting we all tighten our belts – particularly the most vulnerable – because there is no money, there can be no moral justification for giving just one family over £70m. That could pay for a lot of mobility cars.”
She added: “We need to keep taking a step back, look up and look out and see how ordinary people are being shafted by a rich elite and how the odds are always stacked in favour of the most privileged in our society.
“The Sovereign Grant is the epitome of that privilege and a symbol of everything that is rotten at the core of the UK’s political system.”
Alison Thewliss, SNP MP for Glasgow Central said the Crown Estate had amassed profits of £328m from wind farms, money which should be invested in communities instead.
The Scottish Government launched a consultation on the management of the Crown Estate in January, after it was announced control over the assets would be devolved to Holyrood.
The Sovereign Grant currently remains in the control of Westminster.