Tolkien does refer to 'giants' in other works, for example there is Gilim the giant of Eruman in the poem The Lay of Leithian, although Tolkien never finished updating this poem after writing The Lord of the Rings.
And (to mention the obvious) the Ents of The Lord of the Rings could be considered giants -- ent itself is a 'giant word', as is etten in ettenmoors for example.
'As usually with me they grew rather out of their name than the other way about. I always felt that something ought to be done about the peculiar Anglo-Saxon word ent for a ‘giant’ or mighty person of long ago – to whom all old works were ascribed.'
JRRT, letter 157
A large troll could be considered a giant too, especially by a Hobbit; perhaps even a tall Elf or Numenorean could too, from that perspective I guess. Anyway there are references to giants in The Lord of the Rings of course, but I'll leave you to interpret them. For instance...
... the tale revisits, although very briefly, the matter of astonishing news and 'tales' heard in both the Ivy Bush and the Green Dragon, as in the next chapter (Three Is Company):
'Giants and other portents on the borders of the Shire were forgotten for more important matters: Mr. Frodo...'
And later in the story:
'He [Sam] had imagined himself meeting giants taller than trees, and other creatures even more terrifying, some time or other in the course of his journey, but at the moment he was finding his first sight of Men and their tall houses quite enough, indeed too much for the dark end of a tiring day.'
And this interesting passage:
'It was said in ancient days some giants were building The White Mountains as a wall to keep Men out of their land by the sea, one of them called Tarlang tripped and fell on his face as he was carrying a heavy load of rocks on his head he broke his neck and was killed. The other Giants used his body to complete the wall at that point, but left his neck lying southward, leading to the three mountains of the spur Dol Tarlang 'Tarlang's Neck, Cul Veleg 'Big load' and Cul Bin 'Little Load'..
An extract from the second of two versions, Tolkien's Nomenclature of The Lord of The Rings.
Draft texts for The Lord of the Rings
In probably late Sept 1938, or early October 1938, Tolkien will write the chapter Ancient History (partially based on some earlier material), within what is called the 'Second Phase'. This will include the descriptions:
'Trolls of a new and most malevolent kind were abroad; giants were spoken of, a Big Folk only far bigger and stronger than Men the [?ordinary] Big Folk, and no stupider, indeed often full of cunning and wizardry.'
'… But what about these what do you call 'em -- giants? They do say as one nigh as big as a tower or leastways a tree was seen up away beyond the North Moors not long back.' [changed at the time of writing to] 'But what about these Tree-Men, these here -- giants? They do say one nigh as big as a tower was seen up away…'
Of course one can easily find the final versions of both these passages, but in my opinion Tolkien was at least thinking of seemingly 'mannish looking' giants when he first began writing his Hobbit sequel.
The 'giant Treebeard' began as an absolutely towering being! But he was, interestingly enough, drastically reduced in size when he became an Ent (although still notably tall), and then arguably was given a little more height for the final, published version.