Arabs are semites.
The term apparently originated sometime in the early 1800s to describe descendents of the third son of Noah (I think Shem was number 3)...
The prime definition of semite, from American Heritage Dictionary of the English language, is: "A member of a group of Semitic-speaking peoples of the Near East and northern Africa, including the Arabs, Arameans, Babylonians, Carthaginians, Ethiopians, Hebrews, and Phoenicians."
The term anti-semite as referencing a specific bias against Jews didn't enter the language until the late 1800s.
In 1978 Menachim Begin was meeting with, IIRC Anwar Sadat. In the middle of the meeting Begin accused Sadat of being anti-semitic...
Kind of humorous...
But just how that term became so narrowly defined and adopted almost universally to mean anit-Jewish is beyond me. Maybe a good PR team.