The orc dates back to classical times with Pliny the Elder who described an orc as a sea monster - a 'huge creature armed with teeth.' From this, we get today the Orcinus orca, better known as killer whale.

112 eotenas ond ylfe ond orcneas,
Etins and elves and evil-spirits,
113 swylce gigantas/, þa wið gode wunnon
as well as the giants that warred with God
(translation by Francis B. Gummere)

'Orc' was originally seen in English in the epic poem Beowulf (line 112) as 'orc-neas' which has been translated as demon-corpses or zombies. The singular would be 'orc-thyrs' which was found in Old Norse as 'giant'. There are hints at something even older here with the Old English 'orc' meaning demon being related to the Latin word Orca - meaning "hell" or "death". The Romans considered "Orcus" to be the god of death (the act of death - not to be confused with Hades - the realm of the dead). Orcus was also known as "Mors" (mortal, mortuary, etc...) or in Greek, "Thantos".

With one of the linguistic shifts that took place from the original Indo-European, what we are familiar with as 'pork' (from French) from 'porcus' (Latin) lost the leading voiceless aspiration of the 'p' and shows up in Gaelic as 'orc'. This may have lead to some of the pig-nature that shows up some renditions of the modern orc.

Many give credit of the orc to Tolkien who pulled the orc from Old English and twisted the name about (as he often did). "Orc" only appears once in The Hobbit. Christopher Tolkien wrote later

GOBLINS Frequently used as alternative term to Orcs (cf. Melko's goblins, the Orcs of the hills 157, but sometimes apparently distinguished, 31, 230)....
Speculation abounds about why Tolkien switched from using "goblin" to "orc". The most reasonable is that goblins were already well known to people as mischievous faeries such as Puck from Midsummer's Night Dream.
Either I mistake your shape and making quite,
Or else you are that shrewd and knavish sprite
Call'd Robin Good-fellow. Are you not he
That frights the maidens of the villagery,
Skims milk, and sometimes labours in the quern,
And bootless makes the breathless housewife churn;
And sometimes makes the drink to bear no barm;
Misleads night-wanderers, laughing at their harm?
Those that Hob-goblin call you, and sweet Puck.
You do their work, and they shall have good luck,
Are not you he?
(From Midsummer-nights Dream, Act II - Scene 1)