I'm not sure how the degrees are there, but you should try to keep it consistent. If you abbreviate bachelor of science, then abbreviate the master's too. If it's social science I assume it's master of arts? Also, I would capitalise 'Social Science' since it is the name of your degree, so:
'I have a(n) MA degree in Social Science and a BSc degree in Comupter Science.'
The 'n' is in brackets because I think it's personal choice - whether you spell 'MA' or say 'Master of Arts'. Also, if you put a full stop in the abbreviation - M.A., B.Sc. - then do that. I don't know American conventions.