Analytic expressions for speed, flux, microrotation, stress, and couple stress in a micropolar fluid exhibiting a steady, symmetric, and one-dimensional electro-osmotic flow in a uniform cylindrical microcapillary were derived under the constraint of the Debye-Hückel approximation, which is applicable when the cross-sectional radius of the microcapillary exceeds the Debye length, provided that the zeta potential is sufficiently small in magnitude. Since the aciculate particles in a micropolar fluid can rotate without translation, micropolarity affects the fluid speed, fluid flux, and one of the two non-zero components of the stress tensor. The axial speed in a micropolar fluid intensifies when the radius increases. The stress tensor is confined to the region near the wall of the microcapillary, while the couple stress tensor is uniform across the cross-section.