This is one my dad learned at Fort Bragg in the early Seventies, and we always sang it on long trips when I was growing up. It's similar to a different one I've seen on the internet and goes to the tune of "When Johnny comes Marching Home again."

I got a letter from Uncle Sam hurrah hurrah (x2)
I got a letter from Uncle Sam he's sending me to Vietnam
And we'll all be dead by the summer of (insert year)

Other lyrics:
They issued me an M-16. . . and turned me into a fighting machine.

They issued me a bayonette. . . so I could kill without regret.

They issued me an entrenching tool. . . and made me dig like a goddamn fool

They issued me a protective mask. . . and then they threw me in the gas.

They issued me a hand grenade. . . and you should have seen the mess I made.

They shipped me home in a plastic bag. . . the son's of bitches they lost my tags.

They buried me in a deep dark hole. . . They buried me in D.C. but I lived in Idaho.

The moral of the story is. . . to live your life the way it is.
Or we'll all be dead by the summer of (insert year).