You have to distinguish between the two instances of the same table. I will try to help but I'm doing this on a phone...
string updateReq = "UPDATE Student SET Student.ID_Request = R1.ID_Request FROM Request R1 where Student.St_Code=Request.St_Code INNER JOIN Request R2 ON Student.ID_Request = R2.ID_Request";
I can't test this but note that I've given the tables an alias each.