That goes back to the Septuagint. There was a Hebrew word which was an unknown at the time species of animal. In the Septuagint the name given is literally the single horn.
Jerome, in the Vulgate adds a spin to it, he translates some of the occurances of the single horn as unicorn and some as rhinocerous. As is easily seen even in Latin, but you can check the DRB as well since it follows the Vulgate.
When the KJV translators did their translation they went to consistently translating the single horn as unicorn, a literal translation and they put rhinocerous in the footnotes.
If you think when you read unicorn of the mythical horse with a single horn, that wasn’t in view. Unicorn was the name of the single horned rhinocerous.
So basically the KJV translators followed the tradition when one did not understand something in the original language well of following other translations.
You can’t say their translation is really in error for using unicorn without saying both the Vulgate and the DRB are in error as well. Actually the rhinocerous would more be an error than the unicorn since it was effectively and interpretive translation while the unicorn literally followed the Septuagint.
Turns out what was in view was the extinct aurochs which it turns out due to the way their horn looked were evidently called the single horn in Greek. One horn comes up and the horn boss goes right across the top of the head much like a water buffalo and down the other side.
So it’s an interesting linguistic study. But it would be really unfair to single out the KJV translators since every translation from the Vulgate to at least the DRB basically did and followed the same thing. Making a literal or sometimes an incorrect interpretive translation of the Septuagint.
Here are the verses from the KJV
(Num 23:22 kjv) God brought them out of Egypt; he hath as it were the strength of an unicorn.
(Num 24:8 kjv) God brought him forth out of Egypt; he hath as it were the strength of an unicorn: he shall eat up the nations his enemies, and shall break their bones, and pierce them through with his arrows.
(Job 39:9 kjv) Will the unicorn be willing to serve thee, or abide by thy crib?
(Job 39:10 kjv) Canst thou bind the unicorn with his band in the furrow? or will he harrow the valleys after thee?
(Psa 29:6 kjv) He maketh them also to skip like a calf; Lebanon and Sirion like a young unicorn.
(Psa 92:10 kjv) But my horn shalt thou exalt like the horn of an unicorn: I shall be anointed with fresh oil.
DRB
(Num 23:22 DRB) God hath brought him out of Egypt, whose strength is like to the rhinoceros.
(Num 24:8 DRB) God hath brought him out of Egypt, whose strength is like to the rhinoceros. They shall devour the nations that are his enemies, and break their bones, and pierce them with arrows.
(Job 39:9 DRB) Shall the rhinoceros be willing to serve thee, or will he stay at thy crib?
(Job 39:10 DRB) Canst thou bind the rhinoceros with thy thong to plough, or will he break the clods of the valleys after thee?
(Psa 29:6 DRB) And shall reduce them to pieces, as a calf of Libanus, and as the beloved son of unicorns.
(Psa 92:10 DRB) (92:11) But my horn shall be exalted like that of the unicorn: and my old age in plentiful mercy.
JJ