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Galaxy sizes correlate closely with the sizes of their parent dark matter haloes, suggesting a link between halo formation and galaxy growth. However, the precise nature of this relation and its scatter remains to be understood fully, especially for low-mass galaxies. We analyse the galaxy–halo size relation (GHSR) for low-mass ($M_\star \sim 10^{7-9}\, {\rm M}_\odot$) central galaxies over the past 12.5 billion years with the help of cosmological volume simulations (FIREbox) from the Feedback in Realistic Environments (FIRE) project. We find a nearly linear relationship between the half-stellar mass galaxy size R1/2 and the parent dark matter halo virial radius Rvir. This relation evolves only weakly since redshift z = 5: $R_{1/2}\, [{\rm kpc}] = (0.053\pm 0.002)(R_{\rm vir}/35\, {\rm kpc})^{0.934\pm 0.054}$, with a nearly constant scatter $\langle \sigma \rangle = 0.084\, [{\rm dex}]$. While this ratio is similar to what is expected from models where galaxy disc sizes are set by halo angular momentum, the low-mass galaxies in our sample are not angular momentum supported, with stellar rotational to circular velocity ratios vrot/vcirc ∼ 0.15. Introducing redshift as another parameter to the GHSR does not decrease the scatter. Furthermore, this scatter does not correlate with any of the halo properties we investigate – including spin and concentration – suggesting that baryonic processes and feedback physics are instead critical in setting the scatter in the GHSR. Given the relatively small scatter and the weak dependence of the GHSR on redshift and halo properties for these low-mass central galaxies, we propose using galaxy sizes as an independent method from stellar masses to infer halo masses.