Who Wrote the Song You're in the Army Now?

Depends on whether you're referring to the cadence, or to songs by that title. For the cadence, it's rather short:

"Your in the Army now,

Your not behind the clouds,

You'll never get rich you son of a gun,

Your in the Army now"

That's listed as a Vietnam era cadence, and is no longer in use.

As for song lyrics, see the related links at the bottom. The more well known by that name would be the one written by Rob and Ferdi Bolland, and made famous by Status Quo (covers were also done by Laibach and others).

There was also a song by that name penned by the band Macabre.