Tolkien was reportedly a fan of the works of James Fennimore Cooper, and Hawkeye was probably a big influence on Aragorn's development as a character. However, I would suggest that Hawkeye is only one of many influences, and I don't see a lot of particular features of the Ranger class, other than those dealing with woodcraft, that would suggest a strong connection to Hawkeye. The multiple borrowings from the abilities and exploits of Aragorn, on the other hand, are hard to ignore. It seems to me that Aragorn represents a specific crystallization of disparate elements from multiple literary sources which resonated particularly well with the tone of early D&D. No matter what his predecessors looked like, I think it's Aragorn who is being represented by the 1E and earlier Ranger. I can't speak for 2E and on, emphasis on the bow as a weapon, for example, is obviously a departure from both Aragorn and the 1E Ranger, but we still find many elements of the original even in the 5E version of the class.
No argument with that. It's like when a band says, "We were influenced by Metallica." Okay, great. But Metallica in turn clearly drew influence from Led Zepplin. They added their own ideas, but the influence is clear.
Aragorn is a distinctly British kind of Ranger. For example, the idea of being special by birth is totally UN-American. This is the antithesis of the American idea. That's not a negative for LORD OF THE RINGS, it's simply Tolkein putting his particular cultural stamp on an archtype he's building.
That said, I didn't realize we were specifically talking about the OD&D Ranger. When it came out, that class struck me as a Fighter/Thief build. This looks more to the Robin Hood archetype than what the Ranger has become.
The choice by one of my players of that same theme ended up becoming the driving force of my (soon-to-finish) Neverwinter campaign. Oddly enough, he chose it despite playing a barbarian so it's resulted in something of a Conan-esque vibe. (BTW, I think the theme is Neverwinter Noble.)
Did Tolkien create the D&D Ranger?
Next we have the fighting advantage versus "giant class" humanoids. This emulates not only the many battles against orcs throughout the book, but also the climactic event of Aragorn's trajectory as an action hero, the single-handed slaying of a black troll at the Battle of the Black Gate, in which he nearly loses his life. The wounding of the troll's foot as it comes down on Aragorn's throat mirrors the wounding of the heel of Morgoth when he fought with the elven-king Fingolfin in giant form, so it's an important, symbolic moment in the book.