Disc galaxies are typically in a stable configuration where matter moves in almost closed circular orbits. However, non-circular motions caused by distortions, warps, lopsidedness, or satellite interactions are common and leave distinct signatures on galaxy velocity maps. We develop an algorithm that uses an ordinary least squares method for fitting a non-axisymmetric model to the observed two-dimensional line-of-sight velocity map of an external galaxy, which allows for anisotropic non-circular motions. The method approximates a galaxy as a flat disc, which is an appropriate assumption for spiral galaxies within the optical radius where warps are rare. In the outer parts of H I distributions, which may extend well into the warp region, we use this method in combination with a standard rotating tilted ring model to constrain the range of radii where the flat disc assumption can be conservatively considered valid. Within this range, the transversal and radial velocity profiles, averaged in rings, can be directly reconstructed from the velocity map. The novelty of the algorithm consists in using arc segments in addition to rings; in this way, spatial velocity anisotropies can be measured in both components, allowing for the reconstruction of angularly resolved coarse-grained two-dimensional velocity maps. We applied this algorithm to 25 disc galaxies from the THINGS sample, for which we can provide 2D maps of both velocity components.