The radiation damage of the positron source target for the International Linear Collider (ILC) has been studied. The displacement damage in target material due to multi-MeV photons has been calculated by combining FLUKA simulations for secondary particle production, SPECTER data for neutron displacement cross-sections and the Lindhard model for estimations of displacement damage by ions. The radiation damage of a stationary Ti6Al4V target in units of displacements per atom (dpa) has been estimated for photons from an undulator with strength 0.92 and period 1.15 cm. The calculated damage is 7 dpa. Approximately 12.5% of displacement damage result from neutrons.