Yes, molecules have charge and therefore zeta potential. To a light scattering person a molecule is the same as a particle or colloid - a heterogeneity or boundary in the system that allows scattering of light. To a biologist or biochemist there's a difference between a particle and a molecule in solution. One may use diameter and the other radius to describe the effective or equivalent size. To make it clearer, zeta potential is a holistic property of the system - particle or molecule + surrounding solution. Thus external factors such as pH play a very large role in determining the zeta potential. You can look at the change in charge on zwitterionic systems as the pH changes.
Zeta potential is the effective theoretical voltage of a particle, at the 'slipping plane'. The measured parameter is the electrophoretic mobility, and this is often the value more familiar to those working with biomolecules.
Biomolecules and polymers in a buffer/dispersant can in the broadest sense be considered a colloid, and interestingly, the word is derived from the Greek word for glue, i.e. a glue-like substance, also consider the word collagen as a glue-forming substance, and biomolecule.