Dispersion interactions are one of the components of van der Waals forces, which play a key role in the understanding of intermolecular interactions in many physical, chemical and biological processes. The theory of dispersion forces was developed by London in the early years of quantum mechanics. However, it was only in the 1960s that it was recognized that for molecules lacking an inversion center such as chiral and helical molecules, there are chirality-sensitive corrections to the dispersion forces proportional to the rotatory power known from the theory of circular dichroism and with the same distance scaling law R-6 as the London energy. The discovery of the Chirality-Induced Spin Selectivity (CISS) effect in recent years has led to an additional twist in the study of chiral molecular systems, showing a close relation between spin and molecular geometry. Motivated by it, we propose in this investigation that there may exist additional contributions to the dispersion energy related to intermolecular, induced spin-orbit (ISOC) interactions. Within a second-order perturbative approach, these forces manifest as an effective intermolecular spin-spin exchange interaction. Although they are weaker than the standard London forces, the ISOC interactions turn out to be nevertheless not negligible and display the same R$^{-6}$ distance scaling. Our results suggest that classical force field descriptions of van-der Waals interactions may require additional modifications to include the effects discussed here.