World history has been made in Australia, with the installation of the first female Anglican Archbishop.

The Archbishop of Perth, Kay Goldsworthy, says she wants to help restore trust in the institution, which she admits has been harmed by abuse scandals.

Archbishop Goldsworthy has replaced Roger Herft, who retired after admitting he had "let down" abuse survivors in the Diocese of Newcastle, where he had previously served.

In her sermon, Archbishop Goldsworthy reflected on the impact of events examined by the Royal Commission.

"Right now the church's trust bank is pretty depleted. All churches," she said.

"The hurt and grief which has been brought to light has wrapped around us and we find ourselves in totally uncharted waters."

Australia's first female archbishop Kay Goldsworthy knocks on door of St George's Cathedral in Perth as part of her installation service. ( ABC News: David Weber )

The new Archbishop also committed to recognising the importance of Indigenous culture in Western Australia.

"I suspect that no matter how long I am there I will always be aware of both views, both worlds, both realities, one imposed on the other."

"Every story of those first Anglicans and other Christians here is one of balancing precariously.

"Learning new ways to live and tell the story of Jesus, of building churches, schools, offices, community, relationships — and all this set against a background of another world, another culture of more than 40,000 years, and with mixed outcomes."

Archbishop Goldsworthy was one of the first Anglican women to be ordained in Australia.

Then in 2008, in St George's Cathedral, she became a Bishop.

Speaking outside St George's Cathedral after the ceremony, Archbishop Kay remained modest about her achievements.

"There are other women around the world who have done truly amazing things and they simply didn't have the title Archbishop," she said.

"They were bishops or church leaders in various places who have done and continue to do truly amazing things."

Archbishop Kay said her priority would be getting to know the people of Perth as well as regional WA.