We report the confirmation of an old, metal-poor globular cluster in the nearby dwarf irregular galaxy Sextans A, the first globular cluster known in this galaxy. The cluster, which we designate as Sextans A-GC1, lies some 4.4 arcminutes ($\sim1.8$ kpc) to the SW of the galaxy centre and clearly resolves into stars in sub-arcsecond seeing ground-based imaging.We measure an integrated magnitude $V=18.04$, corresponding to an absolute magnitude, $M_{V,0} = -7.85$. This gives an inferred mass $M\sim$1.6$\times10^5~M\odot$, assuming a Kroupa IMF. An integrated spectrum of Sextans A-GC1 reveals a heliocentric radial velocity $v_{\rm helio}=305\pm15$~ km/s, consistent with the systemic velocity of Sextans A. The location of candidate red giant branch stars in the cluster, and stellar population analyses of the cluster's integrated optical spectrum, suggests a metallicity [Fe/H] $\sim$--2.4, and an age $\sim9$ Gyr. We measure a half light radius, $R_h = 7.6\pm0.2$ pc. Normalising to the galaxy integrated magnitude, we obtain a $V$-band specific frequency, $S_N=2.1$. We compile a sample of 1,928 GCs in 28 galaxies with spectroscopic metallicities and find that the low metallicity of Sextans A-GC1 is close to a "metallicity floor" at [Fe/H] $\sim-2.5$ seen in these globular cluster systems which include the Milky Way, M31, M87 and the Large Magellanic Cloud. This metallicity floor appears to hold across 6 dex in host galaxy stellar mass and is seen in galaxies with and without accreted GC subpopulations.

8 pages, 7 figures, 2 tables, accepted for publication in MNRAS after minor revision