My nephew has an American green card. Can you invite me to America?

You can be invited to visit relatives in America, but you can't apply for immigration. Green card can only apply for spouse and minor children to immigrate.

Visiting relatives in the United States: you should provide materials to prove that you have a real and uninterrupted kinship with the inviter, and also consider providing your identity after entering or immigrating to the United States. Relevant documents that are helpful to the application: household registration book or other documents that can prove true kinship, photos taken with relatives in the United States in recent years, copies of American passports or green cards of relatives, copies of passports of relatives staying in the United States for a short time and copies of American visas, etc.