Up above, Roger posted the lyrics from Alan Lomas, The Folk Songs of North America (p. 331), which says it got the song from Our Singing Country (Lomax & Lomax, p. 245). Singing Country has significant differences in the lyrics, and includes a third ('bugle') verse that isn't in Folk Songs of North America:

TEXAS RANGERS

1. Come all you Texas Rangers, wherever you may be,
A story I will tell you which happened unto me.
My name is nothing extry, the truth to you I'll tell,
I am a Texas Ranger, so, ladies, fare you well.

2. It was at the age of sixteen that I joined the jolly band,
We marched from San Antonio down to the Rio Grande.
Our captain he informed us, perhaps he thought it right,
"Before we reach the station, boys, you'll surely have to fight."

3. And when the bugle sounded our captain gave command,
"To arms, to arms," he shouted, "and by your horses stand."
I saw the smoke ascending, it seemed to reach the sky;
The first thought that struck me, my time had come to die.

4. I saw the Indians coming, I heard them give the yell;
My feelings at that moment, no tongue can ever tell.
I saw the glittering lances, their arrows round me flew,
And all my strength it left me, and all my courage too.

5. We fought full nine hours before the strife was o'er,
The like of dead and wounded I never saw before.
And when the sun was rising and the Indians they had fled,
We loaded up our rifles and counted up our dead.

6. And all of us were wounded, our noble captain slain,
And the sun was shining sadly across the bloody plain.
Sixteen as brave Rangers as ever roamed the West
Were buried by their comrades with arrows in their breast.

7. 'Twas then I thought of Mother, who to me in tears did say,
"To you they are all strangers, with me you had better stay."
I thought that she was childish, the best she did not know;
My mind was fixed on ranging, and I was bound to go.

8. Perhaps you have a mother, likewise a sister too,
And maybe so a sweetheart to weep and mourn for you;
If that be your situation, although you'd like to roam,
I'd advise you by experience, you had better stay at home.

9. I have seen the fruits of rambling, I know its hardships well,
I have crossed the Rocky Mountains, rode down the streets of hell,
I have been in the great Southwest where the wild Apaches roam,
And I tell you from experience, you'd better stay at home.


Source: Our Singing Country, John and Alan Lomax, 1941, pp. 245-246

Tune and first stanza from Pauline Farris, Gladys Wilder, Dora Lewis, and Reda West at Liberty, Kentucky, 1937. Singing Country says other verses come from Lomax, American Ballads and Folk Songs, p. 359 - but I can't find it there. The lyrics (no tune) are in John Lomax Cowboy Songs (1916 edition, pp. 44-46) - no significant differences from Singing Country.

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Click to play (Lomax)

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I hope you don't mind that I did some moving around when I consolidated the "Texas Ranger" threads. I kept the "Texas Ranger" song in one thread, and moved all others into the "Songs About the Texas Rangers" thread.