We study the effect of density fluctuations induced by turbulence on the H i/H2 structure in photodissociation regions (PDRs) both analytically and numerically. We perform magnetohydrodynamic numerical simulations for both subsonic and supersonic turbulent gas and chemical H i/H2 balance calculations. We derive atomic-to-molecular density profiles and the H I column density probability density function (PDF) assuming chemical equilibrium. We find that, while the H i/H2 density profiles are strongly perturbed in turbulent gas, the mean H I column density is well approximated by the uniform-density analytic formula of Sternberg et al. The PDF width depends on (a) the radiation intensity-to-mean density ratio, (b) the sonic Mach number, and (c) the turbulence decorrelation scale, or driving scale. We derive an analytic model for the H I PDF and demonstrate how our model, combined with 21 cm observations, can be used to constrain the Mach number and driving scale of turbulent gas. As an example, we apply our model to observations of H I in the Perseus molecular cloud. We show that a narrow observed H I PDF may imply small-scale decorrelation, pointing to the potential importance of subcloud-scale turbulence driving.