I don't think there were any gerim amongst the nevi'im, but would it have been possible?
There is a tradition, recorded in various sources, that the prophet Ovadiah was an Edomite convert. This tradition is born of the fact that there is nothing within his short (one chapter) oracle that concerns Judeans or Israelites; the entire thing is an oracle about the Edomites instead.
- Sanhedrin 39b;
- Tanchuma, Tazria 8.
See also Rashi and Radak on Ovadiah 1:1.
According to R. Yehudah Halevi, a convert cannot be a prophet. The question on R. Yehudah Halevi's view is that Chazal say Ovadiah was a convert. This question, which was raised by the commentators on the Kuzari, is addressed by R. Yitzchak Sheilat who suggests that R. Yehudah Halevi's view depends on a possible dispute in the Gemara about whether Ovadiah was a convert. According to the Rambam, R. Sheilat notes, a convert can certainly be a prophet.
Chananya ben Azur was a prophet (until he went bad), and he was a Givoni, who are a nation of converts (Rashi on Yirmiyah 28:6).
Tana D'Bei Eliyahu: " I testify on Myself heaven and earth, whether man or woman, whether gentile or Jew, whether slaveman or slavewoman, everyone according to his actions, the Ruach Hakodesh (Divine spirit) will dwell on him". from shaarei kedusha available here: http://dafyomireview.com/shaarei_kedusha.php?na=1
(i.e. anyone can reach Ruach HaKodesh even women, slaves, or non-Jews).
as far as being an official prophet, not clear
Not only did Adam and Ḥavah receive prophecy, but so did their son - after murdering his brother - and Noaḥ. And Lot and his family were visited and spoken to by angels. Hagar received prophecy after being exiled, and Pharaoh and his servants received prophetic dreams.
Certainly before Avraham there were no "Jews". Avraham himself "converted", if you can call it that, and so did all of Klal Yisrael, essentially, during the Exodus - and they all received prophecy at Har Sinai.
As for the status of Lot, he was either a "gentile" or a "convert", and the same would have been true of his family.
Similar for Hagar.
Pharaoh and his servants definitely were not Jewish, but, interestingly, Muslims believe that Pharaoh converted at the Sea in order not to drown (and I seem to recall a Midrash or something similar that he converted after everything - does anyone know if I'm making that up?).
The question was specifically about converts becoming Jewish prophets,so here goes:
Sh'maya, Sage and President of the Sanhedrin, from a Mideastern religion
Avtalyon, Sage and Vice-President of the Sanhedrin, from a Mideastern religion
Bithiah, Moshe's foster mother from traditional Egyptian religion
Jethro priest of Midian and father-in-law of Moses from a Mideastern religion
Ruth, great-grandmother of King David, has her own book in the tanach
Osenath, from the Ancient Egyptian religion yoseph hatzadik's wife.
Zipporah, Moses's wife from a Mideastern or northern African religion
Yael, who saved the jews, and was the subject of devorahs song in judges
Onkelos, Hebrew scholar and translator wrote the targum-the only authoritative exposition of the torah(he added stuff), from ancient Roman religion. He spoke to deceased spirits in Gittin-56B, and asked them how israel would fare, then converted.
...were all converts. See any prophets in the list above? Doesn't it say in the Gemara that all tannaim were prophets? I believe Rambam said this as well but don't have the source for it, maybe somebody can add it.