The orc as a trope of modern fantasy originates with Tolkien and Middle-Earth. That being said, Tolkien cited George McDonald and his depiction of goblins in the Princess and the Goblin as a particularly important source of inspiration. Goblin and orc are often used as synonyms or at lease somewhat analogous terms in the Hobbit, though the orcs of his later works, in particular those of the Lord of the Rings are decidedly darker in nature. Beyond McDonald I can't speak with any certainty; goblins tend to be more mischievous than outright demonic in nineteenth century folklore (perhaps /u/itsallfolklore can correct me or clarify on this point). Generally speaking though, the trope seems to be an amalgamation of folkloric elements associated with 'ugly' and at times mean-spirited creatures like trolls and ogres, etc. on top of the literary influences that shaped Tolkien.

However, the word 'orc' has a much older etymological history, deriving from Old English orcþyrs, orcneas, and possibly referring to ogres, evil spirits, etc. (we're not really sure), but ultimately coming from Latin Orcus, the Roman god of death. In The War of the Jewels Tolkien explained:

Note. The word used in translation of Q[uenya] urko, S[indarin] orch, is Orc. But that is because of the similarity of the ancient English word orc, 'evil spirit or bogey', to the Elvish words. There is possibly no connexion between them. The English word is now generally supposed to be derived from Latin Orcus.

And in a letter sent to Gene Wolfe:

Orc I derived from Anglo-Saxon, a word meaning demon, usually supposed to be derived from the Latin Orcus—Hell. But I doubt this, though the matter is too involved to set out here.

One of the more famous references to orcneas comes in the form of a brief name drop in Beowulf:

þanon untydras ealle onwocon

eotenas ond ylfe ond orcneas

swylce gigantas þa wið gode wunnon

lange þrage he him ðæs lean forgeald

---

Thence all evil broods were born,

ogres and elves and evil spirits

--the giants also, who long time fought with God,

for which he gave them their reward

The problem is there are few literary or textual examples of the word in Old English, but Tolkien's general translation of bogey or evil spirit may not be too far off-- though the original word in context likely has little if anything to do with Tolkien's orcs, other than whatever inspiration the author himself drew in choosing it as the name for his creatures.