Yes, but only to the SIAI, due to the standard optimal philanthropy argument.
Oh wait, is there income tax if you work for a charity? In that case, rather than donating, just ask for salary reductions. Use http://lesswrong.com/lw/3kl/optimizing_fuzzies_and_utilons_the_altruism_chip/ to make it still feel like donating, if you find that useful. The only exception is if there is some kind of donation matching that you don't think will reach its limit unless you take your full salary and donate some of it back (or one without a limit - do they do that?). This might cause a conflict of interest though, especially with an unlimited donation matching drive, as SIAI could just give you a $1 million salary and have you donate it all back with donation matching. I can't see any situation in which this won't cause enough bad press to outweigh the monetary benefit, though.
I asked the question because you are already taking a salary reduction by working for SIAI.
I believe that you shouldn't give to charity if you are working for a charity-like cause - at least, not for altruistic purposes. (Many Christian ministers say that one purpose of giving to charity is to help the giver become a better person.)
If you think that SIAI is the best charity, and you work for SIAI, should you give any money to charity?