The plane's registration number is barely visible. Unfortunately it's the best quality I could find.
To answer the question yourself, note that you can see the US flag on the vertical stabilizer and the word "Force" behind the cockpit window. Wikipedia has a list of planes flown by the US Air Force and, although the list is quite long, it is categorized by mission, which cuts down the options quite a lot – the plane obviously isn't a fighter, for example, and, conveniently, "cargo" is early in the alphabet so close to the top of the list.
The serial number 2300 (or 7300?) painted on the nose doesn't correspond to an actual USAF C-17; it was probably temporarily renumbered while filming.