Yes, originally it was the "Caisson Song," based on a real incident in the Philippines at the turn of the last century.  But some years ago the army, always ignorant of tradition, held a contest for new words to the original music and what they came up with was something sappy called "The Army Goes Rolling Along." 

March along, sing our song, with the Army of the free
Count the brave, count the true, who have fought to victory
We’re the Army and proud of our name
We’re the Army and proudly proclaim the Army goes rolling along.

It's like Jody cadence calls with no obscenities, very au courant in today's gender-neutral army.

DavidS wrote Jody cadence calls just don't work without the obscenities. I well remember the calls that began with lines such as, "I got a girl who lives on the hill," and "I don't know but I been told." Don't ask me about the ones you could call in front of your mother, though. The cleanest one I remember is, "Birdie-birdie in the sky/drop some whitewash in my eye./I'm a Marine and I won't cry,/I'm just glad that cows don't fly."

"I don't know but I've been told / Eskimo pussy is mighty cold."  C'mon, Davey, spit it out!