A computational method, based on a moment solution to the discrete dipole approximation (DDA) interaction equations, is proposed for calculation of the T matrix of arbitrary-shaped particles. It is shown that the method will automatically provide the conservation-of-energy and origin-invariance properties required of the T matrix. Furthermore, the method is significantly faster than a T-matrix calculation by direct inversion of the DDA equations. Because the method retains the dipole lattice representation of the particle, it can be applied with relative ease to particles with irregular shapes-although in the same respect it will not automatically simplify for axisymmetric particles. Calculations of scattering matrix distributions, in fixed and random orientations, are made for tetrahedron, cylindrical, and prolate spheroid particle shapes and compared with DDA and extended boundary condition method results.