Is it offensive to call a Jewish person a "semite"?

Is it considered offensive to call a Jewish person a Semite? I've heard the phrase anti-semite or anti-semitism, but I've never heard someone call someone a Semite.

It is not offensive to call someone who is ethnically Jewish a Semite, or rather, offensive is not the best word; it would be better to say it is strange usage:

• 'antisemite' or 'antisemitic', the more common word, is someone or something respectively that has negative ideas about things associated with Judaism the religion, people who are ethnically Jewish (of middle-eastern palestinian descent with other complicated restrictions (and that's just the start of it)) or general cultural things associated with those two.
• 'semite' is (not particularly logically) descended from a large middle-eastern ethnic group, including Jews and Arabs (that's about it). This is an outmoded term
• again not particularly logically, it's just not done to refer to someone who is ethnically Jewish as a Semite, not for any political reasons, but because normally you wouldn't use the outmoded term to refer to Jews and Arabs. You could use it, but people probably wouldn't understand and wonder why you just didn't say 'Jews and Arabs' like a 'normal' person would.

In short, it's not offensive exactly, just kind of weird. Sort of analogous to calling an American (yes, someone from the US) a North American. It would be logically correct, but why would you do that, when you can just say American, Canadian, Mexican or Central American. They are all so different that you wouldn't lump any together or if you knew, you'd specify which country.

The word "semite" is not itself offensive, but it has an awkward, clinical quality that implies some contempt for Jews. Using "semite" suggests that "Jew" is a bad word that needs to be hidden with a more sanitized, formal word. If you don't have any problem with Jews, why not just say "Jew?"

I've heard people object to "African American" (instead of "black") on similar grounds, though obviously there's a broad spectrum of opinion on that one.