I am very much not the best person to answer this question, but:
My understanding is that string theory is a quantum theory, and that means it is not deterministic.
There is a theory of "classical strings"-- remember, strings are just vibrating 1D objects-- which would (since it is classical) be deterministic. However to my knowledge classical string theory is not used in physics. As far as I know it is used just in textbooks to introduce students to the subject, and also as a building block to derive quantum string theory from.
(As an aside: There exist philosophical complications to the claim, as I make above, that "quantum theories are not deterministic". It is possible to create deterministic quantum theories by the use of "hidden variables". For example the "Bohm interpretation" of quantum mechanics uses hidden variables and so is deterministic, in the sense that a "universe sysadmin" with access to the hidden variables could use that knowledge to calculate as you say "what would happen in future". However hidden variable quantum theories have their practical difficulties-- for one thing, they must be nonlocal theories-- and hidden variable theories are not widely used or considered as useful that I have seen. In particular I have never seen anyone attempt to apply hidden-variable interpretation to string theory.)