Galactic disc chemical evolution models generally ignore azimuthal surface density variation that can introduce chemical abundance azimuthal gradients. Recent observations, however, have revealed chemical abundance changes with azimuth in the gas and stellar components of both the Milky Way and external galaxies.To quantify the effects of spiral arm density fluctuations on the azimuthal variations of the oxygen and iron abundances in disc galaxies. We develop a new 2D galactic disc chemical evolution model, capable of following not just radial but also azimuthal inhomogeneities. The density fluctuations resulting from a Milky Way-like N-body disc formation simulation produce azimuthal variations in the oxygen abundance gradients of the order of 0.1 dex. Moreover, in agreement with the most recent observations in external galaxies, the azimuthal variations are more evident in the outer galactic regions. The effect of an analytical spiral structure depends on the pattern speed and the number of spiral arms: larger azimuthal inhomogeneities are found when we consider a slower spiral structure and a single spiral arm. In conclusion we provided a new 2D chemical evolution model capable of following azimuthal density variations. Density fluctuations extracted from a Milky Way-like dynamical model lead to a scatter in the azimuthal variations of the oxygen abundance gradient in agreement with observations in external galaxies.