Yes. At the very least, it seemed to.
‘Bilbo knew no more than he told you, I am sure,’ said Gandalf. ‘He would certainly never have passed on to you anything that he thought would be a danger, even though I promised to look after you. He thought the ring was very beautiful, and very useful at need; and if anything was wrong or queer, it was himself. He said that it was “growing on his mind”, and he was always worrying about it; but he did not suspect that the ring itself was to blame. 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.’
‘Yes, he warned me of that in his last letter,’ said Frodo, ‘so I have always kept it on its chain.’
(LotR, Fellowship of the Ring, Shadows of the Past)
‘A Ring of Power looks after itself, Frodo. It may slip off treacherously, but its keeper never abandons it
(LotR, Fellowship of the Ring, Shadows of the Past)
Isildur also reported that it shrank:
It was hot when I first took it, hot as a glede, and my hand was scorched, so that I doubt if ever again I shall be free of the pain of it. Yet even as I write it is cooled, and it seemeth to shrink, though it loseth neither its beauty nor its shape. Already the writing upon it, which at first was as clear as red flame, fadeth and is now only barely to be read.
(LotR, Fellowship of the Ring, The Council of Elrond)
One size to fit them all
.