Well, a major in political science and international relations is certainly a good start. As N’sMom noted, though, most of these very prestigious international NGOs are going to want people with master’s degrees. (I am also willing to bet that the World Bank and the IMF hires far more economists than they hire people who work directly with refugees).
So yes, a PS/IR major can get you there, but be prepared to have to get graduate education too.
In the U.S., there are lots of organizations that work with immigrants; you could work for a government agency (with pretty much any major) or you could work for a nonprofit or NGO that specializes in helping immigrants. There are a variety of degrees that can help with that; social science majors, social work, public policy and/or administration, and law degrees might be some of the most helpful. I don’t know what the equivalent would be in your country.