It's not clear. There are certainly numerous descriptions of characters wearing armour, but there's far less info about what that actually consists of. For the record, I've been unable to find any use of "plate armour" in any of the novels or supporting materials.
The best I've been able to find is a description of a Haradrim soldier wearing overlapping plates of metal:
Arrows were thick in the air. Then suddenly straight over the rim of
their sheltering bank, a man fell, crashing through the slender trees,
nearly on top of them. He came to rest in the fern a few feet away,
face downward, green arrow-feathers sticking from his neck below a
golden collar. His scarlet robes were tattered, his corslet of
overlapping brazen plates was rent and hewn, his black plaits of hair
braided with gold were drenched with blood. - LOTR: The Two Towers
Based on the description, there seems to be no plate armour in Middle Earth but plenty of lorica segmentata; pieces of metal hung on straps.
There's also some very minor evidence that the dwarves may have had the ability to make and repair scale armour:
Indeed they [dragons] hardly know a good bit of work from a bad, though they
usually have a good notion of the current market value; and they can't
make a thing for themselves, not even mend a little loose scale of
their armour. - The Hobbit