We use a 380-h-1 pc resolution hydrodynamic adaptive mesh refinement (AMR) simulation of a cosmic filament to investigate the orientations of a sample of ~100 well-resolved galactic discs spanning two orders of magnitude in both stellar and halo mass. We find: (i) at z = 0, there is an almost perfect alignment at a median angle of 18°, in the inner dark matter halo regions where the discs reside, between the spin vector of the gaseous and stellar galactic discs and that of their inner host haloes. The alignment between galaxy spin and spin of the entire host halo is however significantly weaker, ranging from a median of ~ 46° at z = 1 to ~ 50° at z = 0. (ii) The most massive galaxy discs have spins preferentially aligned so as to point along their host filaments. (iii) The spin of discs in lower mass haloes shows, at redshifts above z ~ 0.5 and in regions of low environmental density, a clear signature of alignment with the intermediate principal axis of the large-scale tidal field. This behaviour is consistent with predictions of linear tidal torque theory. This alignment decreases with increasing environmental density, and vanishes in the highest density regions. Non-linear effects in the high-density environments are plausibly responsible for establishing this density-alignment correlation. We expect that our numerical results provide important insights for both understanding intrinsic alignment in weak lensing from the astrophysical perspective and formation and evolution processes of galactic discs in a cosmological context.