A judge is not allowed to neglect the justice that is due a convert or an orphan. This is in addition to the general prohibition against perverting justice so that if a judge is derelict in his duty towards a convert or an orphan, he would be in violation of two mitzvos: this one and Mitzvah #233.
The reason for this mitzvah is what we have said before, both about justice and about the downtrodden. Society relies upon the fair implementation of the law; a judge who plays favorites or who bows to political pressure destroys the fabric of the very society he is meant to uphold. Additionally, we have said that converts and orphans lack the support systems that most of us enjoy, so God takes extra interest in their needs. Given all this, a judge would be well-advised not to neglect his duty, especially when it comes to orphans and converts.
This mitzvah applies in all times and places. It is discussed in the Midrash in the Sifre and codified in the Mishneh Torah in the twentieth chapter of Hilchos Sanhedrin. This mitzvah is #280 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #68 of the 194 negative mitzvos that can be observed today as listed in the Chofetz Chaim’s Sefer HaMitzvos HaKatzar.