To the best of my knowdledge, the theatrical cut has never been released on DVD.
Though why anyone would want to actually sit through Battlefield Earth is beyond comprehension to me.
Here's what the IMDb lists as being different:
A scene where Johnny and the other humans try to find instructions to the bomb is added in the U.S. Video and DVD release
In the theatrical release when Terl takes Johnny to the library he tells him that he is sure to find plenty of recipies for raw rat. This has been removed from the US video release.
An early scene of Terl (John Travolta) gleefully rescinding a promise to an unscrupulous underling in a bar/nightclub is cut from U.S. home video prints
In a scene shown in the theatrical version but cut from the video/DVD release, Terl and Ker stand before a chasm with river below. They wonder whether humans can fly or not, and Terl drops one off the edge to see if they can. Humans can't fly, and the man falls screaming into the depths.
In the nightclub scene with Ms. Terl she promises that Terl will be "as happy as a baby Psychlo on a steady diet of kerbango". In the theatrical release the line she delivered was differently phrased and ended in "as happy as a baby in a crib full of Kerbango."