Robbie is seen on the poster wearing a black sweater, white skirt and white boots as she stands in front of a movie theater.
"Hollywood. 1969. #OnceUponATimeInHollywood," Robbie captioned the image.
The ninth film from Pulp Fiction and Reservoir Dogs writer-director Quentin Tarantino is set for theatrical release on July 26.
The movie, which is set against the backdrop of the real-life Manson Family murders in Los Angeles, is slated to screen at France's Cannes Film Festival in May, The Hollywood Reporter said Tuesday.
Best known for her work in the 1967 film Valley of the Dolls, Tate was pregnant and married to filmmaker Roman Polanski when she was stabbed to death by Manson's followers in her home in 1969. She was 26.