Haven't done any research on this myself. But I did look up unicorn in websters 1828 dictionary and here's what it says:
And here are all of the instances "unicorn" is translated in the KJV,
Numbers 23
22 God brought them out of Egypt; he hath as it were the strength of an unicorn.
Numbers 24
8 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.
Deuteronomy 33
17 His glory is like the firstling of his bullock, and his horns are like the horns of unicorns: with them he shall push the people together to the ends of the earth: and they are the ten thousands of Ephraim, and they are the thousands of Manasseh.
Job 39
9 Will the unicorn be willing to serve thee, or abide by thy crib?
10 Canst thou bind the unicorn with his band in the furrow? or will he harrow the valleys after thee?
Psalms 22
21 Save me from the lion's mouth: for thou hast heard me from the horns of the unicorns.
Psalms 29
6 He maketh them also to skip like a calf; Lebanon and Sirion like a young unicorn.
Psalms 92
10 But my horn shalt thou exalt like the horn of an unicorn: I shall be anointed with fresh oil.
Isaiah 34
7 And the unicorns shall come down with them, and the bullocks with the bulls; and their land shall be soaked with blood, and their dust made fat with fatness.