In the final blessing in the series of blessings that comprise Birkot Ha'Torah, we thank Hashem "who has chosen us from all the nation, and has given us the Torah."
The question arises as to whether a Ger (convert) may recite this Beracha, in light of the fact that his ancestors were not among those "chosen" by G-d, and did not receive the Torah. Seemingly, it would be untruthful for a convert to speak of Hashem choosing him and giving him the Torah, since he was not given the Torah, but rather took the initiative to join the Jewish Nation and accept the Torah upon himself.
The Rambam was asked a more general question by a convert named Ovadia, who wondered about numerous different passages in the prayer service that make reference to G-d's having chosen and distinguished the Jewish Nation. He asked, for example, whether he can recite the Berachot which contain the phrase "Asher Kideshanu Be'misvotav" – "who sanctified us with His commands," and whether he can describe G-d in the beginning of the Amida prayer as "Elokenu V'Elokeh Abotenu" – "our G-d and the G-d of our forefathers." As a convert, Ovadia noted, he was not commanded the Misvot, and he was not a descendant of Abraham, Yishak and Yaakob, and so perhaps it would be inappropriate for him to recite these portions of the prayer service. He asked also about the numerous references in our liturgy to G-d having taken us from Egypt, since his ancestors were not enslaved by the Egyptians.
The Rambam responded that converts recite the precise same prayer text as other Jews, without any changes whatsoever. He explains that anyone who converts to Judaism becomes part of the Jewish Nation, and is thus considered a descendant of Abraham, Yishak and Yaakob just like other Jews. As part of the Jewish Nation, he can indeed speak of himself as having been chosen by G-d, having been taken out of Egypt, having been given the Torah, and having been brought to the Land of Israel. Conversion means joining the Jewish Nation, and thus from the moment of conversion he is considered a full-fledged descendant of the patriarchs who experienced all that our ancestors experienced.
We might add that some sources state that all the souls of future converts were present at Mount Sinai when the Torah was given. This concept reinforces the Rambam's view that a convert is considered to have been chosen by Hashem and to have received the Torah.
Therefore, converts recite the same text of Birkot Ha'Torah – and of all other prayers – as other Jews.