"Longstreet's Rangers" was collected in Florida by Alton Morris. Reference to the Rapidan suggests the battle of the Wilderness in 1864. I don't have Morris's book handy, but this is how the song was sung by Hermes Nye on Folkways'"Ballads of the Civil War" (1954):

Come all of Longstreet's Rangers, wherever you may be;
I'll tell you of some trouble that happened unto me.
My name is nothing extra, although I cannot tell.
But after [sic] Longstreet's Rangers, you may know I wish them well.

'Twas at the age of sixteen, I joined our jolly band;
We marched from the Rappahannock unto the Rapidan.
Our captain, he informed us, perhaps he thought 'twas right;
"Before we reach the station," he said, "Boys, you'll have to fight."

I saw the Yankees coming, I heard them give a yell.
My feelings at that moment, my tongue it could not tell;
I saw the smoke ascending, it seemed to reach the sky;
The first thought that struck me was, "Oh, now's your time to die.

We fought them full nine hours before the strife was o'er.
The like of dead and dying I never saw before.
There was five as gallant rangers as ever saw the West;
We buried them by their comrades With bullets in their breast.

And then I thought of mother; these words to me did say,
"You are my only ranger, with me you'd better stay."
But I thought that she was childish, the best she did not know;
My mind was first [sic] on ranging, and I was bound to go.

No Confederate unit was known as "Longstreet's Rangers." However, General James A. Longstreet's army corps included Hood's Texas Brigade, which fought at the battle of the Wilderness. Longstreet lost an arm at the battle.

The Texas Brigade did march "from the Rappahannock unto the Rapidan"
in Virginia, but they did so by way of Gettysburg, Pa., and Knoxville, Tenn.!