Handbag released the promo, which shows Hall as a 30-something ex-dancer who sets out to pursue her dream of being a cocktail waitress in Las Vegas.
After arriving in Vegas she meets charming gambler Dink (Bruce Willis), who recruits her as his good luck charm, which galls Dink's wife (Catherine Zeta Jones).
Lay the Favourite is released in the UK on June 22, and had its US premiere at the Sundance Film Festival earlier this year.
Hall is reportedly in talks to join the cast of Iron Man 3, after Jessica Chastain officially dropped out.
Watch Rebecca Hall speaking to Digital Spy about her last film The Awakening below: