This compares to 30.1 per cent of Australians who have no religion, 22.6 per cent who are Catholic and 13.3 per cent who are Anglican.
The poll of 1200 voters found that 45 per cent of voters believe the number of immigrants coming to Australia should be reduced, with 23 per cent arguing for a rise and 29 per cent happy with the status quo.
When asked about the number of immigrants from Muslim countries, 46 per cent supported a cut while 35 per cent were happy with current levels and 14 per cent wanted an increase.
The poll comes as Prime Minister Scott Morrison considers possible changes to Australia's immigration system.
Mr Morrison in September signalled plans to slow the intake of some temporary migrants and to encourage new arrivals to settle outside of congested major cities.
On Monday, Defence Minister Christopher Pyne said the government will be sticking to its non-discriminatory immigration policy.
"We have a non-discriminatory policy, that must remain in place ... we need to manage our population growth sensibly in a country which quite frankly can take a lot more than 25 million people," Mr Pyne told Sky News.
Last month, NSW Premier Gladys Berejiklian has called for a return to Howard-era immigration levels of about 45,000 a year.
Meanwhile, the poll also revealed that Mr Morrison's coalition government trails Labor by 48 per cent to 52 per cent on a two-party preferred basis.
But Mr Morrision remains the preferred prime minister, with a 47 per cent to 35 per cent lead over Opposition Leader Bill Shorten.
On energy policy, the poll found that voters want the government to focus on reducing household bills (47 per cent), followed by reducing carbon emissions (39 per cent).
The National Energy Guarantee was declared "dead" by Mr Morrison after becoming prime minister, but the government has recently floated the idea of underwriting a new power generation project to help s to drive prices down and increase competition.