The promo spotlights Casey Affleck and Rooney Mara as two lovers torn apart.
Bob Muldoon (Affleck) and Ruth Guthrie (Mara) are a couple on the run from the law. When Ruth shoots a police officer, her lover takes the blame and goes to prison for four years.
When Bob gets out of prison, he finds that the mother of the daughter he has never met has fallen for another man (Ben Foster).
Keith Carradine, Rami Malek and Nate Parker will also feature in David Lowery's drama.
The film premiered to great acclaim at the Sundance Film Festival earlier this year.
Ain't Them Bodies Saints will arrive in US cinemas on August 16. A UK release date is yet to be set.