The idea of magic jewelry - and magic rings specifically - far predates Tolkien. As an early example, Plato's The Republic features a story about the Ring of Gyges which confers invisibility on the wearer. There are also quite a few magic rings in Arabian Nights, mostly pertaining to controlling djinn.

Throughout the medieval romances there are a fair number of jewelry pieces with magical effects, such as early versions of Sir Perceval having a ring that makes the wearer unable to die, and Gareth having a similar ring of invulnerability in *Le Morte d'Arthur". In The Knight of the Lion Sir Yvain has a magic ring which grants invisibility when worn a certain way (stone on top of his hand is normal, stone pointed down towards his palm makes him invisible).

The connection to Tolkien likely comes from his study of Norse mythology. Odin has a magical arm ring, Draupnir, for example. In addition there have been archaeological finds of rings with runic inscriptions, most notably the Kingmoor Ring and the Bramham Moor Ring which both include the runes ærkriu, which based on comparisons with similar words found in the c. 9th Century medical text Bald's Leechbook likely have to do with stopping the flow of blood; working theory is that the inscriptions were meant to be charms to protect the wearer.

However Tolkien wasn't the one who brought Norse magic rings to wider public attention. That honor would go to composer Richard Wagner, who wrote a cycle of four operas first released between 1869-1876 called Der Ring Des Nibelungen, or The Ring of the Nibelung, or simply as The Ring Cycle. In this story there is a magic ring which grants the power to rule the world.

As a specific example from the early-mid 1900s, see comics. Green Lantern's Power Ring was first written about in 1940. Wonder Woman's bracers (1941) were made by Aphrodite to be indestructible, and are able to deflect bullets and energy blasts.

In short, Tolkien didn't create the idea of magic jewelry. Had he not been born, the idea of magic rings would still be around, just perhaps not as ubiquitous as today due to, as you put it, the impact of LOTR on fantasy in general.

Oh goodie! I get to pull out my copy of Playing at the World.

If you don't know, Playing at the World by Jon Peterson is a scholarly examination of Dungeons & Dragons which delves into absolutely every cultural aspect of the original game. He has a section on magic items that I am going to draw liberally from here.

Peterson's general contention is that the elements of fantasy in D&D are not primarily drawn from Tolkien. Instead the main attributions tend to by that of Jack Vance, Fritz Leiber, and Robert E Howard's Conan the Barbarian. These stories tend to feature far more exaggerated uses of magical elements which were more relevant to a systemic interpretation. For instance, an early Conan story features a healing potion and many other tales feature scrolls with temporary magic effects.

On the subject of jewelry, Peterson identifies a few different rings of power that predate Tolkien's use of the motif in The Hobbit. In Arabian Nights, the character Aladdin uses a ring which binds the spirit of a djinn just as the lamp does. The Ring of Djinn Summoning is an item in the original version of D&D. King of the Golden Mountain, one of the Grimm's Fairy Tales, has a ring which grants wishes as well as a cloak of invisibility, serving as a possible Tolkien inspiration. The Castle of Iron, a contemporary book of The Hobbit, has a ring that can protective from magic, as in the Ring of Spell Turning from the D&D item list.

The general motif of empowered accessories is also explored in other fantasy media. The Dying Earth, Bleak Shore, and Doctor Strange all feature magical amulets which serve as wards against malevolent magic. This general concept is seen across many cultures, from early Christian talismans to Nordic runes to Native American dreamcatchers.

The idea of objects which can ward off unseen forces is very ingrained in culture. Expressing that in the reverse, through objects which can instill curses or actively grant power is a bit more taboo, but can be observed in the veneration of Christian saints. The idea that not only did the bones of a saint hold sacred power, but things which touched them could as well, was easily transferable to create holy relics which could be used as tools of European leaders.

What are the legends of the Holy Grail, the Lance of Longinus, or the Shroud of Turin if not magical items? They don't have concrete effects like those in fantasy stories, but the conception behind them is the same. It's highly likely that the early fiction authors of the current age were drawing upon such motifs for their ideas of enchanted artifacts. It's not exclusive to Christianity - obviously Norse mythology has weapons imbued with properties and that influenced Der Ring des Nibelungen - it's just a useful example when attempting to determine this question.

Perhaps a deeper question would be "Why jewelry?" There's obviously a royal connection there, though neither Der Ring des Nibelungen nor Lord of the Rings attempt to tie it purely to noble lines. It might just be a matter of practicality. How can power be permanently imbued in someone without having them lose it accidentally? The idea of simply "blessing" someone with power is very abstract. Storytellers gravitate towards the concrete. Plus it becomes possible to remove that power should the story call for it. A piece of jewelry is a perfect solution in that sense.

I approached this question first from the D&D side because it obviously was the route from which it trickled down into games and generally broader pop culture as "default" fantasy. The general concept of enchanted jewelry did not necessarily come from Tolkien and the broader idea of enchanted artifacts is far older than the fantasy genre. Many fantasy authors came to the concept and D&D codified it as something which was systemic and consistent rather than vague and mysterious.