The reconstruction problem in diffraction tomography is addressed for cases where noise-free scattering data are available for a limited number of view angles (discrete set of incident wave directions). The solution to the inverse problem (reconstruction problem) is obtained in the form of an iterative method known in the literature as Kaczmarz's method and is found to be a generalization of the algebraic reconstruction technique (ART) of conventional computed tomography (CT) to diffraction tomography (DT). The generalized ART algorithm is shown to generate a reconstruction that is consistent with the data and that has minimum L² norm along all such solutions. A computer simulation is presented comparing the performance of the algorithm with the filtered backpropagation algorithm.