When molecules are aggregated such that their excited states form delocalized excitons, their spatial arrangement, or packing, can be coarsely controlled by templating and finely controlled by chemical substitution; however, challenges remain in controlling their packing on intermediate length scales. Here, we use an approach based on mechanically interlocked molecules to promote an elusive oblique packing arrangement in a series of three squaraine rotaxane dimers. We template the squaraine rotaxane dimers using DNA and observe two excitonically split bands of near-equal intensity in their absorption spectra – a distinct signature of oblique packing, validated by theoretical modeling of the experimental results. Additional fine control of packing is demonstrated by fluorinating the macrocycle of the rotaxane, which promotes denser packing and stronger excitonic interactions.