Effects of turbulence on ice supersaturation at cirrus heights (>8 km) remain unexplored. Small-scale mixing processes become important for high Reynolds number flows, which may develop below the buoyancy length scale (10-100 m). The current study couples a stochastic turbulent mixing model with reduced dimensionality to an entraining parcel model to investigate, in large-ensemble simulations, how supersaturation evolves due to homogeneous turbulence in the stably stratified, cloud-free upper troposphere. The rising parcel is forced by a mesoscale updraft. The perturbation of an initially homogeneous vertical distribution of supersaturation is studied after a 36-m ascent in a baseline case and several sensitivity scenarios. Turbulent mixing and associated temperature fluctuations alone lead to changes in ensemble-mean distributions with standard deviations in the range 0.001-0.006, while mean values are hardly affected. Large case-to-case variability in the supersaturation field is predicted with fluctuation amplitudes of up to 0.03, although such large values are rare. A vertical gradient of supersaturation (≈10⁻³ m⁻¹) is generated for high turbulence intensities due to the development of a dry-adiabatic lapse rate. Entrainment of slightly warmer (less than 0.1 K) environmental air into the parcel decreases the mean supersaturation by less than 0.01. Supersaturation fluctuations are substantially larger after entrainment events with an additional small offset in absolute humidity (by ±3.5%) between the parcel and environmental air. The predicted perturbations of ice supersaturation are significant enough to motivate studies of turbulence-ice nucleation interactions during cirrus formation that abandon the assumption of instantaneous mixing inherent to traditional parcel models.