The Greens bill, to be introduced next week, would limit rent increases to the rate of inflation.
"Rent prices are skyrocketing out of control. At the moment, South Australian renters are at the mercy of the market and a housing system that's stacked against them," Greens upper house MP Robert Simms said on Tuesday.
"We need rent controls to ensure that renters are protected.
"Rent increases of 10 to 20 per cent are crippling for families. Without reform, I fear more South Australians will be plunged into poverty and homelessness."
Data from the SA Housing Authority earlier this month showed there had been a 20 per cent increase in rental prices during the past two years.
On average, rents have risen from $350 to $420 a week and there is no cap on increases by landlords.
Mr Simms said many places around the world had rent controls including New York, Ireland and Spain.
Premier Peter Malinauskas said he was not across the detail of the bill but would look at the Greens' proposal.
But he said it was important any changes did not affect private investment in more housing.
"We should be alive to the fact that quick fixes don't always solve the problem," the premier said.
"But we welcome all suggestions and we'll have a close look at Mr Simms' bill."
Mr Malinauskas said there was no doubt there was a national housing and rental affordability crisis.
He said as a rich country Australia could do better to provide assistance to those in need and governments had a role to play to increase the availability of public housing.
The Greens' move on rents comes after a welfare group called for urgent action by the state government to ease housing issues.
The Anti-Poverty Network said the government should massively expand public housing stocks and improve the rights of tenants, including longer and more secure leases, and the right for renters to keep pets.
It also called for a moratorium on evictions, similar to that during the height of the COVID-19 pandemic, to stop renters losing their homes as the cost of living soars.
"While the new state government has committed to building an extra 400 public homes over four years, with 17,000 people on the public housing waiting list and over 7000 people experiencing homelessness, this commitment falls massively short of what is needed," group spokesperson Pas Forgione said.
"Moreover, no commitments have been made to limit the huge and unsustainable rises in private rents we have repeatedly seen, or strengthen the rights of tenants."
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