Clinical manifestations of cystic fibrosis (CF) result from an increase in the viscosity of the mucus secreted by epithelial cells that line the airways. Particle-tracking microrheology (PTM) is a widely accepted means of determining the viscoelastic properties of CF mucus, providing an improved understanding of this disease as well as an avenue to assess the efficacies of pharmacologic therapies aimed at decreasing mucus viscosity. Among its advantages, PTM allows the measurement of small volumes, which was recently utilized for an in situ study of CF mucus formed by airway cell cultures. Typically, particle tracks are obtained from fluorescence microscopy video images, although this limits one's ability to distinguish particles by depth in a heterogeneous environment. Here, by performing PTM with high-resolution micro-optical coherence tomography (μOCT), we were able to characterize the viscoelastic properties of mucus, which enables simultaneous measurement of rheology with mucociliary transport parameters that we previously determined using μOCT. We obtained an accurate characterization of dextran solutions and observed a statistically significant difference in the viscosities of mucus secreted by normal and CF human airway cell cultures. We further characterized the effects of noise and imaging parameters on the sensitivity of μOCT-PTM by performing theoretical and numerical analyses, which show that our system can accurately quantify viscosities over the range that is characteristic of CF mucus. As a sensitive rheometry technique that requires very small fluid quantities, μOCT-PTM could also be generally applied to interrogate the viscosity of biological media such as blood or the vitreous humor of the eye in situ.