Job 39:9-12 (King James Version)
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?
11.Wilt thou trust him, because his strength is great? or wilt thou leave thy labour to him?
12.Wilt thou believe him, that he will bring home thy seed, and gather it into thy barn?
Yep, god is talking to Job about a unicorn.
Isaiah 34:7 (King James Version)
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.
See, according to the superstitious hebrews of the day, unicorns were every bit as real as a bull.
Psalm 29:6 (King James Version)
6.He maketh them also to skip like a calf; Lebanon and Sirion like a young unicorn.
They were real enough to the superstitious tribal people that they could compare a calf to a unicorn.
In context, it is clear that these references are not in some mythical non-existing fashion, but that they really believed this singled horned magic creature of legend was real. Not something made up, but real and really existed. For the bible to be real and perfect, that means that we have to accept that unicorns are real and exist.
Or, we can acknowledge that unicorns didn't exist and are fairy tales. Just like the whole of the bible itself. Fairy tale myths born from a superstitious people in a time of superstition before science existed.
For your pleasure, here are some other scriptures that mention unicorns.
Numbers 23:22 (King James Version)
22.God brought them out of Egypt; he hath as it were the strength of an unicorn.
Deuteronomy 33:17 (King James Version)
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.
Psalm 22:21 (King James Version)
21.Save me from the lion's mouth: for thou hast heard me from the horns of the unicorns.
Psalm 92:10 (King James Version)
10.But my horn shalt thou exalt like the horn of an unicorn: I shall be anointed with fresh oil.
As we can see, the tribal peoples were very much believers in these mythical creatures. And apparently, so was god.