Is there any racism against black people in the army?
No more than there is racism anywhere else. Yes you may encounter some. just as you would encounter some in the Civilian world. There is also racism by black against whites both in and out of the military. If you are going to refuse to join because you may encounter racism. you may as well check yourself out of Civilian life too. Or are you just using the possibility of racism as an excuse? Truth be told if you are looking to avoid racism then join the military. you are less likely to encounter it within such a proffesional organization as the US military than you are in the Civvy world.