The theory of the discrete-dipole approximation (DDA) for light scattering is extended to allow for the calculation of radiation forces on each dipole in the DDA model. Starting with the theory of Draine and Weingartner [Astrophys. J. 470, 551 (1996)] we derive an expression for the radiation force on each dipole. These expressions are reformulated into discrete convolutions, allowing for an efficient, O(N logN) evaluation of the forces. The total radiation pressure on the particle is obtained by summation of the individual forces. The theory is tested on spherical particles. The resulting accumulated radiation forces are compared with Mie theory. The accuracy is within the order of a few percent, i.e., comparable with that obtained for extinction cross sections calculated with the DDA.