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. Deuteronomy 33:17 (KJV)

Save me from the lion’s mouth: for thou hast heard me from the horns of the unicorns. Psalm 22:21 (KJV)

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. Isaiah 34:7 (KJV)

Yes. Let me explain before you pull out your magical pixie dust.
The animal described above is not the mythological horse with one horn. The verses above are from the King James translation of the Bible completed in 1611. The Hebrew word is re’em, which means “one horn.” The modern translation of “unicorn” is wild oxen. The explanation has a number of possible meanings. Some oxen have been discovered with one horn. Some say if you look at the oxen from the side it has one horn. Whatever the animal was, I’m sorry to say it was not the fantasy horse from literature.

So the early Bible translation says unicorns exist, but not the same unicorn we imagine.