Since the Book of Psalms was written in Hebrew, let's look at what Hebrew language and Bible scholars say on the subject. Specifically with regards to Psalm 22:21 (verse 22 in some Bibles), it says:
"Save me from the lion's mouth; yea, from the horns of the רמים[plural version; pronounced "reymim"]."
This is an animal that appears elsewhere in the Bible. For example, Numbers 23:22 states:
God brought them out of Egypt, He has as though the lofty horns [תועפֹת] of a רְאַם [singular, pronounced "re'em"].
From this verse and its reference to "horns" we can see that the רמים have two horns, not one. It is hard to understand the Septuagint's translation of that phrase, however, which, instead of "lofty horns of the רְאַם" it says it means "the glory of a unicorn." Rabbi David Kimhi (the "Radak"), in his commentary to the verse, and others adopted the Septuagint’s translation and explained the רְמֵם to be a single-horned animal. Rav Saadiah Gaon also seems to follow this view, translating the רְאַם in this verse as the karkadan, which is the name of the unicorn in Arabian legend. But although the Septuagint defines the רְאַם as an animal with a single horn, Scripture itself in another verse indicates that it possesses more than one horn:
His firstborn ox, grandeur is his, and his horns are like the horns [קַרְנֵי] of a רְאַם; 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 Menasheh (Deuteronomy 33:17). Even with this verse, Radak continued to hold that a רְאַם had just one horn, but his view was rebutted by Rabbi Eliyahu Ashkenazi, in his response to Radak, who said that the animal does have two horns and is therefore not a unicorn.
The above analysis, by Rabbi Nathan Slifkin, one of the most prominent authors on Biblical references to exotic animals, in an article titled "Exotic Shofars: Halachic Considerations," goes on to determine that the ראם is a type of cow, citing additional Biblical verses and Talmudic authority.