We have developed the linear theory of collisionless ion tearing in a two-dimensional magnetotail equilibrium for a single resonant species. We have solved the normal mode problem for tearing instability by an algorithm that employs particle-in-cell simulation to calculate the orbit integrals in the Maxwell-Vlasov eigenmode equation. The results of our single-species tearing analysis can be applied to ion tearing where electron effects are not included. We have calculated the tearing growth rate as a function of the magnetic field component Bn normal to the current sheet for thick and thin current sheets, and we show that marginal stability occurs when the normal gyrofrequency Ωn is comparable to the Harris neutral sheet growth rate. A cross-tail By component has little effect on the growth rate for By ≃ Bn. Even in the limit By ≫ Bn, the mode is strongly stabilized by Bn. We report that random pitch angle scattering can overcome the stabilizing effect of Bn and drive the growth rate up toward the Harris neutral sheet (Bn = 0) value when the pitch angle diffusion rate is comparable to Ωn.