Yes. A person who converts to Judaism is fully Jewish. Jewish tradition is clear that a Jew by choice should never be treated as anything less, and JSLI welcomes Jews by choice to study with us and be ordained as rabbis and cantors.
Converts bring something special
Many of the most devoted Jews in any community are people who chose Judaism as adults. They came to it with open eyes, studied hard, and made a commitment most born Jews never had to make out loud. That experience can make for a wonderful rabbi, especially one serving interfaith families and seekers, who often relate easily to someone who walked that road. Ruth, the great-grandmother of King David, is the model here.
What’s required
Jews by choice apply the same way as everyone else. You’ll need to read siddur Hebrew and have a working knowledge of Jewish history, texts, holidays, ritual and lifecycle, and you’ll have a personal interview with the Dean. Some movements and institutions have their own policies about which conversions they recognize, so if you plan to serve a particular community, it’s worth asking about that early.
If your conversion was recent and you’d like more grounding first, our Mechina preparatory year is a good place to start. See also Who Can Become a Rabbi?