Atmospheric turbulence can cause random variations of the refractive index, resulting in a spatial inhomogeneity. When a high order Bessel Gaussian beam is propagating through the atmospheric turbulence, spatial inhomogeneity can bring about the change of photon wave function that causes the disperse of the orbital angular momentum to form different photon states. Under the Rytov approximation, when the high order Bessel beam was propagating in a slant-path atmospheric turbulence, the weight of the spiral harmonic component of the beam energy was calculated. And then, the impact on the spiral spectrum of the beam propagating in the slant ways, caused by refractive index structure constant, the wavelength of the beam, the zenith, orbital angular momentum, the receiver aperture, spot size were discussed and compared and a series of concrete explanations were given. The research results show that with increasing refractive index structure constant and the zenith and with decreasing wavelength of the beam, the spectrum of the spiral harmonic main component reduces and the orbital angular momentum disperses more serious. The receiver aperture and spot size have little effect on the orbital angular momentum disperse.