Terahertz (THz) wireless communications have the potential to realize ultra-high-speed and secure data transfer with miniaturized devices for unmanned aerial vehicle (UAV) communications. Existing THz channel models for aerial scenarios assume a homogeneous medium along the line-of-sight propagation path. However, the atmospheric turbulence due to random airflow leads to temporal and spatial inhomogeneity of the communication medium, motivating analysis and modelling of the THz UAV communication channel. In this paper, we statistically modelled the scintillation and attenuation effect of turbulence on THz UAV channels. Specifically, the frequency- and altitude-dependency of the refractive index structure constant, as a critical statistical parameter characterizing the intensity of turbulence, is first investigated. Then, the scintillation characteristic and attenuation of the THz communications caused by atmospheric turbulence are modelled, where the scintillation effect is modelled by a Gamma-Gamma distribution, and the turbulence attenuation as a function of altitude and frequency is derived. Numerical simulations on the refractive index structure constant, scintillation, and attenuation in the THz band are presented to quantitatively analyze the influence of turbulence for the THz UAV channels. It is discovered that THz turbulence can lead to at most 10dB attenuation with frequency less than 1THz and distance less than 10km.