My father is arranging relatives to immigrate to America. Can I apply for graduate study in the United States?

Of course ~ follow the normal process of applying for a master's degree in the United States. When I get the I-20 of the school, I will go to the American Embassy to apply for a visa according to the identity and preparation materials of F 1. The question answered is also about your own study abroad, which has nothing to do with your father's green card schedule.

Of course, whether to apply for a green card after actually entering the United States is another matter. But it will not affect your application and entry into the United States for a master's degree.