'Anti-Semite'

Who coined this phrase? Where was it first used?

This page says

According to Wikipedia, the German version of the word (“antisemitismus”) was coined by Wilhelm Marr in 1873. He used it to describe prejudice against Jews on racial grounds (as opposed to prejudice on religious grounds, for which the word “Judenhass” already existed).

I don’t know when the word crossed over into English.

Wilhelm Marr, in 1873

1881 is the first recorded use in English found by the OED.