Political Sciences. One of my friends is aspiring to become an ambassedor, he went that way. His father was also the ambassador to a couple of countries.
Its not feasible for everyone to have connections and once one does have connections he/she has to have a background, so studying International Relations, and Political science like Ganja and Who---Me suggested is a good idea, as well it would be best if the individual studies Development Studies which are broken into diverse geographical subjects at certain Universities such as South Asia Development Studies, etc.