His father, John Shipton, accepted the document at a Darlington celebration today.
He says his son's been jilted by the Australian government, and the passport ceremony - which follows Ecuador's decision to grant Mr Assange diplomatic asylum - is a show of solidarity.
Indigenous Social Justice Association president Ray Jackson says the Australian government hasn't given Mr Assange sufficient aid.
The passport will be sent to Mr Assange in London in the next few days.
John Shipton, Assange's biological father, said he spoke frequently with the 41-year-old who won asylum from Ecuador to escape extradition from Britain to Sweden, where he faces sexual assault allegations.
"He's in a small room... and in that he has a treadmill and a sunlamp," he told AFP in Sydney's Redfern where he had accepted an Aboriginal Nations passport, for use when travelling within Australia, on behalf of his son.
"But he faces his future with equanimity. He says he may have to spend 12 months in this situation. I think that he's prepared himself for his long meditation."
Shipton, 68, said his son was still pressing ahead with his plans to run for the Australian Senate in the national election due next year, and had asked his father to write the constitution for his yet-to-be founded political party.
Sydney-based Shipton said he felt Australians were "genuinely concerned and moved" by the plight of Assange and the work of WikiLeaks, which has published hundreds of thousands of documents online, including confidential United States State Department emails.
He said he had spoken to Assange about the Aboriginal Nationals passport -- used for travel through Aboriginal lands in the country.
"This occasion is a further opportunity to generate support for Julian's situation," he said.
"The irony is it's a great help to bring to notice to people that the situation is well, very questionable, morally very questionable.
"The (Australian) foreign minister could do a little more. Although he says he has done a lot, he won't speak to me."
Shipton, who said he had always kept in touch with Assange's mother but had little contact with his son from when he was three until his twenties, spoke of his pride in Assange, a former computer hacker.
"I am astounded, absolutely astounded. And each day more impressed," he said.
"He seems as though he handles himself at those rarefied atmospheres really quite well.
"It must have taken a great deal of suffering to have learned so quickly how to move amongst those people... and not display fear when the whole American empire wishes to crush you."
But Shipton won't be watching a new movie about Assange's earlier life called "Underground: The Julian Assange Story" which is set to screen on Australian television early next month. He doesn't have a television.