Q. Is there a mitzvah to accept proper gerim?

A. From Talmud (Yebamot 47: 2) it would seem that there is a mitzva to accept gerim, since the Gemara mentions in regards to the immediate circumcision of a ger: “We do not delay a mitzva.” So rules the Raved, who declares it to be a mitzva on the Beis Din. (Ba’alei Nefesh – end of Shaarei Tevila).
Tashbatz (Zohar Harakia 40) maintains that the mitzva to accept gerim is included in the precept of “Veahavtem es Hager” (loving the proselyte).
Hagr’Y. Perlo (on S’Mag 19) opines that the mitzva of gerus is part of the commandment of “Loving Hashem” (Devarim 6: 5) as quoted in Sifri on that posuk.
However, Devar Avrohom (2: 25) asserts that it is not a compulsory mitzva, but rather similar to shechita, if one wants to eat meat, he has to sacrifice the animal as the Torah ordained. Igrois Moishe (Y.D. 3: 109), in regards to a specific case, writes that it is a “great mitzva” to convert that particular woman. Kol Tzofaich (p.503) debates whether a Beis Din that delays unnecessarily the gerus process, transgresses on a positive commandment.
Horav Shlomo Miller’s Shlit”a opinion is that the Beis Din complies with this mitzva, at the end of the process.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a