  In this paper, we study the entanglement entropy in string theory in the
simplest setup of dividing the nine dimensional space into two halves. This
corresponds to the leading quantum correction to the horizon entropy in string
theory on the Rindler space. This entropy is also called the conical entropy
and includes surface term contributions. We first derive a new simple formula
of the conical entropy for any free higher spin fields. Then we apply this
formula to computations of conical entropy in open and closed superstring. In
our analysis of closed string, we study the twisted conical entropy defined by
making use of string theory on Melvin backgrounds. This quantity is easier to
calculate owing to the folding trick. Our analysis shows that the entanglement
entropy in closed superstring is UV finite owing to the string scale cutoff.
