With the deepening of atmospheric turbulence research, scientists have discovered that the anisotropy of turbulence cells cannot be ignored. The anisotropic non-Kolmogorov turbulence model is more in line with the actual situation of atmospheric turbulence. However, the recent experimental results of Korotkova et al. and Beason et al. display that the turbulence cell has an anisotropic tilt angle, that is, the long axis of the turbulence cell may not be horizontal to the ground but has a certain angle with the ground. Therefore, it is urgent to analyze whether the anisotropic tilt angle is necessary in the turbulence spectrum. In this study, we develop the anisotropic non-Kolmogorov turbulence spectra for the horizontal and vertical links in the presence of the anisotropic tilt angle. Then, based on these spectra, the analytical expressions of the scintillation index for the horizontal and vertical links are derived under weak fluctuation condition. The results indicate that the anisotropic tilt angle is necessary in the vertical link but not in the horizontal link.