Any non-Jew can become a Jew by converting. Once he converts, he then becomes a Jew in every regard and his relationship with God is the same level as that of every other Jew.
Unlike many other religions, Judaism does not demand that all people convert to the religion. Maimonides explains that any human being who faithfully observes the "7 Laws of Noah" earns a proper place in heaven. The Torah of Moses is a truth for all humanity, whether Jewish or not.
As well, the Holy Temple did not just benefit Jews. When King Solomon built the Temple, he specifically asked God to heed the prayer of the non-Jew who comes to the Temple (1-Kings 8:41-43). The Jewish prophet refers to the Temple as a "House for all nations" (Isaiah 56:7). The Temple was the universal center of spirituality, a concentrated point where God-consciousness filtered down into the world.
In ancient times, the service in the Holy Temple during the week of Sukkos featured a total of 70 bull offerings. This, the Talmud explains, corresponds to each of the 70 nations of the world. In fact, the Talmud says that if the Romans (who destroyed the Temple) would have realized how much benefit they themselves were benefiting from the Temple, they never would have destroyed it!
But what about the non-Jew who does wish to convert to Judaism? According to the Code of Jewish Law (the "Shulchan Aruch"), there are three requirements for a valid conversion. The requirements are:
1) Mitzvahs ― He must believe in God and the divinity of the Torah, as well as accept upon himself to observe all 613 mitzvahs (commandments) of the Torah.
2) Milah ― Male converts must undergo circumcision by a qualified "Mohel." If he was previously circumcised by a doctor, he then undergoes a ritual called "hatafas dam".
3) Mikveh ― All converts must immerse in the Mikveh ― a ritual bath linked to a reservoir of rain water.
All of the above must be done before a court of three Jewish men who themselves believe in God, accept the divinity of the Torah, and observe the mitzvahs.
The conversion must be motivated for the sole purpose of getting close to God and His Torah, and not for ulterior motives such as money or marriage.
It is inadvisable for anyone to convert until he is able to accept the responsibilities a true conversion would entail.
There are two excellent books on the topic of conversion:
There are two excellent books which are helpful for conversion: