We have used the Watson-sphere-terminated molecular-cluster model within the framework of the multiple-scattering X\ensuremath{\alpha} theory to carry out electronic-structure calculations of a carbon substitutional impurity in GaAs. The activation energy of the ${\mathrm{C}}_{\mathrm{As}}$ impurity level is calculated as a function of inward symmetrical displacements of the nearest-neighbor Ga atoms. The center is found to be a shallow acceptor, and it is shown that an inward relaxation of the Ga atoms is expected. Unlike other group-IV elements, such as Si and Ge, carbon replacing Ga in GaAs is found to be a deep center.