Etymology
The earliest recorded uses of the word were in 1900 and 1904.
The source of the term is uncertain, but the Encyclopedia of Swearing stated the most reasonable and most likely origin of the term is the one proposed by Leo Rosten, according to whom:
The word kike was born on Ellis Island when there were Jewish migrants who were also illiterate (or could not use Latin alphabet letters). When asked to sign the entry-forms with the customary "X", the Jewish immigrants would refuse, because they associated an X with the cross of Christianity. Instead, they drew a circle as the signature on the entry-forms. The Yiddish word for "circle" is kikel (pronounced KY-kul), and for "little circle", kikeleh (pronounced KY-kul-uh). Before long the immigration inspectors were calling anyone who signed with an "O" in place of an "X" a kikel or kikeleh or kikee or, finally and succinctly, kike.
According to the Oxford English Dictionary, it may be an alteration of the endings –ki or –ky common in the personal names of Jews in eastern Europe who immigrated to the United States in the early 20th century.
A variation or expansion of this theory published in Our Crowd, by Stephen Birmingham, postulates that the term "kike" was coined as a put-down by the assimilated U.S. Jews from Germany to identify eastern European and Russian Jews: "Because many Russian [Jewish] names ended in 'ki', they were called 'kikes'—a German Jewish contribution to the American vernacular. The name then proceeded to be co-opted by non-Jews as it gained prominence in its usage in society, and was later used as a general derogatory slur."
Compounding the mysterious origin of this term, in 1864 in the UK the word ike or ikey was used as a derogatory term for Jews, which derived from the name "Isaac", a common Jewish name.
Usage
Some sources say that the first use was on Ellis Island as a term for Jewish people, others that it was used primarily by Jewish-Americans to put down Jewish immigrants.
In a travel report from 1937 for the German-Jewish publication Der Morgen, Joachim Prinz, writing of the situation of Jewish immigrants in the USA, mentions the word as being used by Jews to refer contemptuously to other (Eastern) Jews:
Es ist nicht erhebend zu sehen, wie verworren die Vorstellungen sind, wie wenig die Einwanderer gelernt haben, wie glücklich sie teilweise sind, dem Juden-schicksal entsprungen zu sein, und wie überheblich sie oft sind. Es macht traurig, daß sie in manchen Kreisen sehr unbeliebt sind, und man wundert sich über die Dummheit derer, die die Ostjuden (von denen sie ja doch gestützt werden!) verächtlich „Kikes‟ nennen […]