There is a good chance both adjectives can be used here (depending on the extent to which this individual is lacking in his social skills), but what would typically be the phrasing used about a person who brings up risqué topics at civilized social gatherings, asks another person in the company of strangers how much s/he earns, comes out with personal remarks where these are uncalled for, etc.?
Would you say "He has undeveloped social skills" or "He has underdeveloped social skills"?
I believe Underdeveloped is what you're looking for. Undeveloped would imply that he has not developed any social skills at all. But since he is not likely to be a neanderthal or raised by wolves, he probably has some social skills. Just not very well developed social skills. In other words, he has underdeveloped social skills.
Hey! Sounds like you and I probably attended the same school, tdol!
Oh well, the fact that you and I are now communicating through a website focusing on proper English usage must indicate we came from a good batch!