The possibility of measuring scattering-matrix (Mueller matrix) elements of soot agglomerates with laser diagnostic techniques is explored. To show this, we calculated the scattering-matrix elements of arbitrary-shaped soot agglomerates. The sensitivity of scattering-matrix elements to optical and morphological characteristics of fractal-like soot agglomerates is discussed. Finally, possible measurement techniques are suggested to identify soot structures from scattering-matrix elements.