When answering to another question on this site related to A Song of Ice and Fire by G.R.R. Martin, another user pointed out a site where it is possible to perform searches on the full texts of the published works by that author, namely A Search of Ice and Fire.
I was wondering if there is a similar tool for the works of J.R.R. Tolkien, where one can search his whole corpus of published works for a given term.
The closest thing I can think of is The Tolkien Text Anthology.
It is an offline resource, but it has all of the works of J.R.R. Tolkien (including some of the rarer ones like Vinyar Tengwar and Parma Eldalamberon) in a single interface designed for searching.
I doubt it's any more legal than A Search of Ice and Fire though.
To the best of my knowledge, there is no search-engine like portal for Tolkien's published works. There have been many efforts to digitize some of the more popular ones (you can purchase e-books, of course, and the Internet Archive has a few in text-searchable form1), which would allow you to assemble one for yourself (Valorum's suggestion, in a comment on the question), but there are notable gaps in what's available.
The most notable are writings published in issues of Vinyar Tengwar and Parma Eldalamberon, special interest newsletters published by the Elvish Linguistic Fellowship fan group. Both publications have received permission from Christopher Tolkien to publish essays (primarily language-related), but few exist in digitized form. It's this kind of limitation that dooms any attempt to create a "complete" Tolkien search engine: so many of his writings came into existence long before digitization was a thing, and weren't commercial enough to convert.
In theory there's nothing stopping someone from setting up an "incomplete" search engine (aside from the usual legal questions), just focused on the most "narrative" books, but to my knowledge nobody has done it; if they have, it certainly isn't prominent.
While not remotely what you're looking for, an interesting quasi-example is the Eldamo lexicon, which is a reasonably-complete online dictionary of Tolkien's invented languages drawing from most of Tolkien's published word-lists.
1 I'm unclear on the legal implications of this, which is why I'm not posting links
Search engine, no... But there is a concordance, which is almost as good? But it might just be for ''The Hobbit''?
an alphabetical index of the principal words in a book or the works of an author with their immediate contexts
