Of course, '시' is pronounced as '시'. :)
To give a more helpful answer, you are correct in that ㅅ in '시' is similar to English "sh", or more precisely, IPA symbol [ʃ]. (Edit: it's apparently [ɕ], which is a similar(?) but different sound.)
However, note that [ʃ] in English is usually pronounced with rounded lips, so the English word "she", for example, will be perceived more like 쉬 than 시 by a Korean speaker.
As Vladhagen said, the most common Romanization scheme currently in use ("Revised Romanization" as wikipedia calls it) uses 's' for all occurrence of ㅅ, when it starts a syllable. It actually makes sense: you don't want the transliteration of a language to show differences of a sound that a native speaker perceives as the same ("allophones"): it would be like trying to write "pin" and "spin" using two different versions of p's, because only "pin" is aspirated (a distinction which most English speaker is oblivious of, because their brains choose the correct sound automatically).
Another scheme that used to be popular, the McCune–Reischauer (MR), does make the distinction: so 시 will be written as 'shi' using MR.