Many come up with the same date and coiner when you use DuckDuckGo. The one I pasted was Encyclopedia Britannica.

Wikipedia also dates it back to the 1800s, but different. Though used as the same purpose.

The origin of "antisemitic" terminologies is found in the responses of Moritz Steinschneider to the views of Ernest Renan. As Alex Bein writes: "The compound anti-Semitism appears to have been used first by Steinschneider, who challenged Renan on account of his 'anti-Semitic prejudices' [i.e., his derogation of the "Semites" as a race]."[15] Avner Falk similarly writes: "The German word antisemitisch was first used in 1860 by the Austrian Jewish scholar Moritz Steinschneider (1816–1907) in the phrase antisemitische Vorurteile (antisemitic prejudices). Steinschneider used this phrase to characterise the French philosopher Ernest Renan's false ideas about how 'Semitic races' were inferior to 'Aryan races'".[16]