The Bible says they do or at least did did, Num 23:22 God brought them out of Egypt; he hath as it were the strength of an unicorn.
Num 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.
Job 39:9 Will the unicorn be willing to serve thee, or abide by thy crib?
Job 39:10 Canst thou bind the unicorn with his band in the furrow? or will he harrow the valleys after thee?
Psa 29:6 He maketh them also to skip like a calf; Lebanon and Sirion like a young unicorn.
Psa 92:10 But my horn shalt thou exalt like [the horn of] an unicorn: I shall be anointed with fresh oil.