If you are specifically talking about the sicillian-american mafia (cosa nostra), your father has to be italian for you to become a full-fledged member. In some more traditional cosa nostra families, both of your parents have to be italian. however, you can still be an associate but not a member if you are not italian. this is just specific to the cosa nostra. membership requirements differ to each organized crime group. However, I do not recommend joining an organized crime group because you have a higher chance of being murdered/arrested. but you can do whatever you want.