We present a novel method for the determination of the internal structure of macromolecular aggregates in solution based on polarized absorption measurements on magnetically aligned aggregates. Different types of aggregates of three cyanine dyes were investigated in order to test the method. The obtained stacking geometries agree with those found by X-ray diffraction experiments on single crystals grown from the studied dyes, providing evidence that our method is a valuable tool for structural analysis of molecular assemblies.