Shalom, Is there a halakha that prohibits bnei noach from studying the torah?
In general if a gentile wants to do mitzvos, he may, except for two mitzvos that a gentile may not do. These are torah learning and keeping Shabbos. regarding torah learning the Gemora (Sanhedrin 59a) says that it is prohibited for a gentile to study torah, and one who does do is chayav missa. Also see Rambam Hilchos Melachim 10-9. There are numerous reasons for this as written in the introduction to the the sefer תורתך לישראל, a sefer that is dedicated to this topic. A gentile may however study the seven Noahide Mitzvos – which are applicable to him. He may also learn Nevi’in and Kesuvim, and he can learn Bible on his own, (but a Jew should not teach it to him) See Torasecha L’yisroel Chaoter 1).