  We use multi-wavelength SDSS images and Galaxy Zoo morphologies to identify a
sample of $\sim$$270$ late-type galaxies with an off-centre bar. We measure
offsets in the range 0.2-2.5 kpc between the photometric centres of the stellar
disc and stellar bar. The measured offsets correlate with global asymmetries of
the galaxies, with those with largest offsets showing higher lopsidedness.
These findings are in good agreement with predictions from simulations of
dwarf-dwarf tidal interactions producing off-centre bars. We find that the
majority of galaxies with off-centre bars are of Magellanic type, with a median
mass of $10^{9.6} M_{\odot}$, and 91% of them having $M_{\star}<3\times10^{10}
M_{\odot}$, the characteristic mass at which galaxies start having higher
central concentrations attributed to the presence of bulges. We conduct a
search for companions to test the hypothesis of tidal interactions, but find
that a similar fraction of galaxies with offset bars have companions within 100
kpc as galaxies with centred bars. Although this may be due to the
incompleteness of the SDSS spectroscopic survey at the faint end, alternative
scenarios that give rise to offset bars such as interactions with dark
companions or the effect of lopsided halo potentials should be considered.
Future observations are needed to confirm possible low mass companion
candidates and to determine the shape of the dark matter halo, in order to find
the explanation for the off-centre bars in these galaxies.
