Much fakelore surrounds the song "Texas Rangers."
It possibly refers to the Battle of Stone Houses, which took place in 1837 near present-day Windthorst, north-central Texas. This, the only engagement fought by Texas Rangers in which there was significant loss of Rangers, was the result of stupidity.
Rangers under Capt. Wm. Eastland pursued a band of Kichai Indians up the Colorado River, but lost the trail. An argument ensued between Capt. Eastland and Lt. Van Benthusen and the company separated. Van Benthusen and seventeen men headed north up the Brazos River and contacted the Indians. Cherokees and Delawares who were present tried to act as peace agents, but Ranger Felix McClusky jumped an Indian and killed him. When reprimanded, McClusky replied that he would kill any Indian for a plug of tobacco and showed one he had taken from the dead Indian's body. The angered Indians attacked and the Rangers abandoned their horses and holed up in a ravine. Fighting ensued for two hours, until the Kitchais set fire to the prairie to smoke them out. The Rangers charged through the smoke and into the woods. Four Rangers were killed in battle and six during the escape. Eight of the seventeen made it on foot to Sabine Settlement. From Handbook of Texas Online: Stone Houses

The song varys in the number of Rangers killed, six to 16 in most versions; no Captain died.
The verse in the DT about 300 noble rangers dead may refer to some action by the Eighth Texas Cavalry under Terry during the Civil War, but is certainly not the result of a Texas Rangers engagement. The cavalry unit, a mixed group, included some rangers, but Terry never had been a ranger.

The song most likely was written sometime after the Civil War. Reputedly it surfaced in 1874 (Traditional Ballad Index) and an earlier origin is claimed, but there is no proof of this. Because of the similarity of the versions, a newspaper printing is a likely source.

I would not be surprised to find that the following version, from a woman who came to Indian Territory in 1885 from Kentucky, is closer to the original than those detailing the deaths of rangers.

THE DISHEARTENED RANGER

Come, listen to a ranger, you kindhearted stranger,
This song, though a sad one, you are welcome to hear;
He has kept the Comanches away from your ranches,
And followed them far on the Texas frontier.

He is weary of scouting, of traveling and routing
The bloodthirsty brutes o'er prairie and wood;
No rest for the sinner, no breakfast, no dinner,
No rest from his suffering bed in the mud.

No corn nor potatoes, no beets nor tomatoes,
The jerked beef's as dry as the sole of your shoes;
All day without drinking, all night without winking,
I'll tell you, kind stranger, this never will do.

Those great alligators, the state legislators,
Are puffing and blowing two-thirds of the time,
But windy ovations about rangers and rations
Never put in our pockets one-tenth of a dime.

They do not regard us, they will not reward us,
Though hungry and haggard with holes in our coats;
But the election is coming, and they will be drumming
And praising our valor to purchase our votes.

For glory and payment, for victuals and rainment,
No longer I'll fight on the Texas frontier;
So guard your own ranches, and mind the Comanches
Or surely they'll scalp you in less than a year.

Though sure it may grieve you, the ranger must leave you
Exposed to the arrow and knife of the foe;
So look to the cattle and fight your own battle,
For home to the States I am determined to go.

Where churches have steeples and laws are more equal,
Where churches have people and ladies more kind,
Where work is regarded and worth is rewarded,
Where pumpkins are plentiful and pockets relined.

Thanks for listening to the ranger, you kindhearted stranger,
This song, like the ranger is now at an end;
So guard your own ranches, and mind the Comanches
Or surely they'll scalp you in less than a year.

The song seems to refer to the Frontier Battalion of the Texas Rangers, 1874-1882, composed of six companies with 75 rangers each, which, under Maj. John B. Jones, participated in 15 Indian battles in 1874. Together with the United States Cavalry, they ended the Commanche-Kiowa threat in 1875, and "thinned out" more than 3000 Texas desperados, including Sam Bass and John Wesley Hardin. The Frontier Battalion was no longer necessary after 1882. Information from Handbook of Texas Online.
With music, sung by Mrs. Lula Sublet of Fort Gibson, OK; born in Kentucky and came to Indian Territory in 1885. Ethel and Chauncey O. Moore, 1964, "Ballads and Folk Songs of the Southwest," no. 151, pp. 315-316.