Would the One Ring work if it was worn on someone’s toe instead of their finger?
Depends what you mean by work.
The ring has power even when not being worn.
In The Lord of the Rings orcs are scared by the presence of the ring
It stopped short aghast. For what it saw was not a small frightened hobbit trying to hold a steady sword: it saw a great silent shape, cloaked in a grey shadow, looming against the wavering light behind; in one hand it held a sword, the very light of which was a bitter pain, the other was clutched at its breast, but held concealed some nameless menace of power and doom.
Later Sam has a vision of the power the ring holds while being worn around Frodo's neck.
Then suddenly, as before under the eaves of the Emyn Muil, Sam saw these two rivals with other vision. A crouching shape, scarcely more than the shadow of a living thing, a creature now wholly ruined and defeated, yet filled with a hideous lust and rage; and before it stood stern, untouchable now by pity, a figure robed in white, but at its breast it held a wheel of fire. Out of the fire there spoke a commanding voice. ‘Begone, and trouble me no more! If you touch me ever again, you shall be cast yourself into the Fire of Doom.’ The crouching shape backed away, terror in its blinking eyes, and yet at the same time insatiable desire.
If you mean "would you turn invisible if you put it on your toe (or other appendage)1" the answer is probably yes, but we can't be sure as we never see a Toe-ring of power
- Possibly outside the remit of this site
I say yes.
There was nothing to suggest that the ring's power was limited to working when it was on someones finger.
Being that ring can change in size to suit the bearer
Though he had found out that the thing needed looking after; it did not seem always of the same size or weight; it shrank or expanded in an odd way, and might suddenly slip off a finger where it had been tight.’
So , if one were to put it on their toe, you could only assume that it would change size to fit the toe.
As for it working while being worn on the toe, a toe an appendage just like a finger and there is nothing to show in the LOTR that it shouldn't.
Tolkien mentions in a letter that a fish eating the ring would be overcome with desires to take over the world... and would die floundering on the shores of the river. If eating the thing affects the eater then wearing it on a different appendage would be a lesser change. However all this is based on a reading of a letter on a blog about 7 years ago...