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)?
Yes, the only limitation is that the conversion is recognized by the Jewish Agency and the Ministry of Absorption. Having your conversion recognized by the Ministry of Absorption can be either easier or harder than having it recognized by the Chief Rabbinate of Israel depending on the situation.
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.