  The recently introduced anomaly-free twistor string in four dimensions is
shown to be defined not just in flat but also in curved twistor space. Further,
arguments are given that the classical limit of the corresponding string field
theory, if it exists, is related to general relativity, in particular to the
Isenberg and Yasskin construction using teleparallel gravity. For spacetimes of
Petrov type D with two shear-free null congruences the construction can be
simplified using two-dimensional twistor manifolds.
