I was wondering if a convert (someone who was not born a Jew) may, by the rules of the state of Israel, migrate to Israel (make aliyah, as defined by the State of Israel)?
Israel's Law of Return says that
Every Jew has the right to come to this country as an oleh.
and defines "Jew" as
a person who was born of a Jewish mother or has become converted to Judaism and who is not a member of another religion.