A prominent Indigenous rights activist and politician has officially become Australia's first female Aboriginal MP, giving her maiden speech in the House of Representatives Wednesday.

The Wiradjuri woman and former teacher was "sung in" by fellow Wiradjuri women in a powerful display of traditional culture.

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Delivering her first speech as Labor member for the New South Wales seat of Barton in Sydney's south, Burney donned a kangaroo skin cloak featuring her clan totem, the goanna, and her personal totem, the white cockatoo, which she described as "the noisy messenger bird."

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"I was born at a time when the Australian Government knew how many sheep there were but not how many Aboriginal people. I was 10 years old before the 1967 referendum fixed that," she said, referring to the year Indigenous Australians were finally counted as citizens.

She told the story of her upbringing, included being negatively stereotyped by teachers and townspeople, and recognised the impact her position could have on inspiring young Aboriginal and Torres Strait Islanders. "If I can stand in this place, so can they — never let anyone tell you, you are limited by anything."

Linda Burney is vocal about being "committed to social justice and the feminist cause" and hopes to be "part of the parliament which sees the First Peoples recognised in our constitution."

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Australia's government includes only one other Aboriginal member in the House of Representatives, Ken Wyatt AM who is of Yamatji, Wongi and Nyoongar heritage.

When Burney's speech was over, Wyatt, who represents the opposing Liberal party, gave her an emotional hug.

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Watch the full speech, below.