I've heard two ways of pronouncing this word; "A" feeling more common than "B."
I've included a link of me pronouncing the word "Social" in the two different ways I've heard.
http://soundcloud.com/jmnixon95/social-social
First time around, the emphasis is on the difference I hear in the two pronounciations. (The "ci" part of the word, basically.) Then the second time is more like how you would hear the word in conversation.
I do understand that other accents may pronounce the "ci" part of the word slightly differently than the ways I did, but if this is a terrible problem for you, just think, "Which sounds more correct with an American accent..."
Ignoring the unnatural emphasis, which way do you find more "correct?"