The 'Maleficent' actress, 49, and the 16-year-old, got the same inking after they worked together on The Outsiders Broadway show in tribute to one of the mother-of-six's lines in the production.
She told CR Fashion Book: "I got 'Stay Gold' with my daughter Viv during our time with The Outsiders. It means so much to us separately and together."
Angelina, who has five other children with her estranged ex-husband Brad Pitt, 60, added she also shares a bird tattoo with some of her other kids, which she says they have for "personal" reasons.
Recent photos have shown Jolie has 'Stay Gold' inked in red on her inner arm, but it is unclear is Vivienne has her version of the tattoo in the same spot.
Jolie produced The Outsiders, which is based on S E Hinton's 1967 book of the same name, and hired the teen as her assistant for the show.
She said about the decision: "Viv reminds me of my mother in that she isn't focused on being the centre of attention but in being a support to other creatives.
"She's very thoughtful and serious about theatre and working hard to best understand how to contribute."
Jolie also has children Maddox, 23, Pax, 20, Zahara, 19, Shiloh, 18, and Vivienne's twin Knox, 16, with Pitt.
She showed off another new tattoo of a bird she has on her chest at the 2024 Tony Awards in June.
It featured a black outline of a swallow, which is said to represent loyalty and the love of home due to the species' migration habits.
Jolie is still battling Pitt over her sale of her chunk of their French vineyard.
Her actor father Jon Voight, 85, recently said he wishes the pair's divorce battles would "be over".
The Midnight Cowboy actor told Fox News Digital: "I wish that would be over. It's tough. I wish they found a way to make peace."
Voight added he is worried about how the warring couple's legal woes has affected his grandchildren, adding: "I think that the kids need some stability. I love the kids and I love my daughter, and I want Brad to step up, too (and do) what he has to do (and) end this nonsense."
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