The singer and Waititi, who split from his wife Chelsea Winstanley in 2018, first sparked rumours they were dating in April this year when Ora posted a series of photos of the pair on Instagram captioned, "Good times, memories, random things on my phone and the ones I love".
The couple were then spotted together at the RuPaul's Drag Race premiere in Sydney, where the director had been filming his next Marvel film Thor: Love and Thunder.
In May, the singer reportedly moved to Sydney to live with her boyfriend, with the pair making headlines not long afterwards when they were snapped with Thor actress Tessa Thompson.
Photos of Waititi kissing Ora, his rumoured girlfriend, and Thor actress Tessa Thompson went viral on social media.
The Daily Mail, which published the photos, reported the images were snapped at Waititi's house after a party.
Twitter users speculated the three stars may be in a polyamorous relationship, but it could have been a prank to throw off the paparazzi.
They celebrated Waititi's 46th birthday last month and are said to be talking about getting married. Last month, they appeared on their first red carpet together at the premiere of Suicide Squad in Los Angeles.
According to New Idea, the writer and director calls his girlfriend, 30, "wifey" and "chats about how he's going to be her first and last husband".
The source continued, "Everyone around them downplays it as flirty banter, but [Rita is] definitely hoping he's for real."