Can a non-Jew marry a Jewish Israeli in Israel?

No. There is no legal mechanism in Israel to solemnize a marriage between a Jew and a non-Jew within the country. The Chief Rabbinate only performs marriages between two Jewish partners, and the other religious courts only handle marriages within their own communities. The practical solution used by many thousands of couples each year is to marry in a country with civil marriage — Cyprus is the most common choice for its proximity and simplicity — and then register the marriage with Israel's Ministry of Interior. The registered marriage carries full legal effect in Israel.