Your question is a little tricky. Tolkien's Rangers of the North were a nomadic people, building no permanent settlements and living off the land, there have been numerous such tribes, though Tolkien may have been specifically drawing off the Irish Travelers.

But what it sounds like you want to know is if individual wandering protectors of forests and wildlife with bows and animal companions and 4 levels of divine spellcasting were a thing. And the answer to that question is yes (except for the companions and spells, I think the real rangers probably got bonus feats instead).

In order to tell you about rangers, let's start with a quick old-school linguistics lesson that's completely irrelevant to us today! A bunch of trees all in one place is woods (sometimes a woods, but that's an uncommon syntax). A forest (a word we're certain is of Latin origin, but that linguists seem unclear what the original meaning was, I'm familiar with at least three separate etymologies, but most likely derives from 'foresti', meaning 'absent', or 'foris', referring to a boundary between inside and outside such as a door or gate) is a specific area, not always woods, covered by William the Conqueror's Forest Laws.

Before the Norman Conquest, certain areas were designated as royal hunting grounds, most notably by Cnut:

"And I will that every man be entitled to his hunting in wood and in fields, on his own possessions; and let everyone forego my hunting. Beware where I will have it untrespassed under penalty of full 'wite' (fine). "

Under William, certain parcels of land (most notably the 'New Forest'in Hampshire and Wiltshire) were deemed forests, meaning that a different set of laws applied on them than everywhere else, essentially setting up something very similar to a modern government-protected forest (not protected for its own sake as those are, but like Cnut, protect for the king's sake as his own personal hunting ground). The Forest Laws ennumerated offenses against 'the vert' (plants) and 'the venison' (animals, including at least red deer, fallow deer, roe deer, and wild boar, but I've seen lists that included other animals such as foxes, hares, partridges, and pheasants) in protected forests. Such animals could only be hunted with the king's permission (which may or may not have been available for a fee, this seems to have varied over the years). The protection of the vert made it illegal to chop trees as well as clearing or burning plants.

I'll admit I wasn't able to find a primary source for William's original forest laws when I wrote about this subject years ago and I still can't today. The earliest primary source I can find is the 1217 Charter of the Forests, I should be interested if anybody does have a reliable source for earlier laws.

There were a variety of laws, and they were only expanded over time. Of course, laws don't enforce themselves, you need somebody to actually catch people in the act. These people included verderers, appointed by and answerable directly to the county sheriff, who investigated and prosecuted forest crimes, foresters and keepers who performed daily patrols and and arrested forest criminals, and regarders who would perform yearly inspections for the king.

And that brings us back around to your question. Although Tolkien's rangers were nomads rather than officials working for any government or in any specific forest, this is where he would have gotten the basic idea.