How can I immigrate my cousin with his sister, mom and aunt together from jordonto the USA

It is unlikely you will be able to help them immigrate. Only certain persons can petition for an alien to receive an immigrant visa. You can petition for a spouse, parent, child, unmarried son/daughter, or sibling. You cannot petition for a cousin. Your parent would be able to petition for his/her sibling. You can read more about family immigration at http://myattorneyusa.com/family-immigration.