Although there is no problem with a convert being a great Torah scholar, as the examples of Shmayah and Avtalyon as well as Onkelos ha-Ger and many others amply demonstrate, there may be a problem with appointing a convert as the rabbi of a community. This question is addressed directly by [R. Nosson Gestetner][1], who [concludes][2] that a convert cannot receive the title "Rav" although he may be the one to whom the community turns to answer their questions. 

R. Moshe Feinstein does not address this exact question. Nevertheless, he expresses a lenient inclination. Here is a free translation of what R. Moshe Feinstein says about whether a convert can become a Rosh Yeshiva ([Iggeros Moshe YD 4:26][3]):

> The simple answer, based on the Gemara in Kiddushin 76b... and Yevamot
> 45b... and the Rambam Hil. Melachim 1:4... is that it is forbidden to
> appoint a convert for a position of authority for Jews... But you [the
> questioner] wanted to prove based on Shmayah and Avtalyon and others
> [that it is permitted]--however, besides for the fact that we don't
> know exactly what there lineage was [whether their mother was a born
> Jew], one cannot bring a proof from them because they were the
> greatest of their time...and who knows if it was not a temporary
> exception [hora'at sha'ah], like the case of the prophet Devorah who
> was a judge (see Tosafos Bava Kama 15a...and Yevamot 45b...) and how
> can we compare our case to theirs.

> But practically, one must know
> that the commandment to love the convert (Deut. 10:19) obligates us to
> bring them close, and to be lenient in all these types of issues.
> Therefore, after much consideration, it seems that we only consider
> appointments in our time to be those that have [real] authority, but
> the role of a Rosh Yeshiva is to teach students who want to learn...

  [1]: http://www.hebrewbooks.org/pdfpager.aspx?req=50287&st=&pgnum=131&hilite=
  [2]: http://www.hebrewbooks.org/pdfpager.aspx?req=50287&st=&pgnum=136
  [3]: http://www.hebrewbooks.org/pdfpager.aspx?req=14679&pgnum=257