"If u love this one as much as we do, get the soundtrack," the singer also tweeted.
The video features key scenes from the film, showing Ally (Gaga) meeting Cooper's character Jackson Maine, and them embarking on their whimsical journey together. The music video also offers snippets from the movie of the duo performing at festivals and recording the song in the studio.
Check out the mid-tempo track below!
WATCH: A Star Is Born's Lady Gaga and Bradley Cooper in the new video for their song Shallow