AsSalaamu 'Alaikum, is it permissible to travel back to America after making hijrah for the purpose of marriage?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

If you are asking about traveling to America for the purpose of completing the arrangements of your marriage and then returning to your Muslim country, this is permissible on condition that you travel with a Mahram man. That is because a Muslim woman is not allowed to travel without a Mahram as authentically narrated in the Sunnah of the Prophet, sallallaahu ‘alayhi wa sallam.

But if you want to stay in America after marriage, the ruling depends on certain details that scholars mentioned in this regard. You may review this in Fatwa 86405.