We present new HI observations from the Australia Telescope Compact Array and deep optical imaging from OmegaCam on the VLT Survey Telescope of NGC 1427A, an arrow-shaped dwarf irregular galaxy located in the Fornax cluster. The data reveal a star-less HI tail that contains ~10 per cent of the atomic gas of NGC 1427A as well as extended stellar emission that shed new light on the recent history of this galaxy. Rather than being the result of ram pressure induced star formation, as previously suggested in the literature, the disturbed optical appearance of NGC 1427A has tidal origins. The galaxy itself likely consists of two individual objects in an advanced stage of merging. The HI tail may be made of gas expelled to large radii during the same tidal interaction. It is possible that some of this gas is subject to ram pressure, which would be considered a secondary effect and implies a north-west trajectory of NGC 1427A within the Fornax cluster.