In Galactic halo stars, sulphur has been shown to behave like other {alpha}-elements, but until now, no comprehensive studies have been done on this element in stars of other galaxies. Here, we use high-resolution ESO VLT/FLAMES/GIRAFFE spectra to determine sulphur abundances for 85 stars in the Sculptor dwarf spheroidal galaxy, covering the metallicity range -2.5<=[Fe/H]<=-0.8. The abundances are derived from the SI triplet at 9213, 9228, and 9238{AA}. These lines have been shown to be sensitive to departure from local thermodynamic equilibrium, i.e. NLTE effects. Therefore, we present new NLTE corrections for a grid of stellar parameters covering those of the target stars. The NLTE-corrected sulphur abundances in Sculptor show the same behaviour as other {alpha}-elements in that galaxy (such as Mg, Si, and Ca). At lower metallicities ([Fe/H]<~-2) the abundances are consistent with a plateau at [S/Fe]=~+0.16, similar to what is observed in the Galactic halo, [S/Fe]=~+0.2. With increasing [Fe/H], the [S/Fe] ratio declines, reaching negative values at [Fe/H]>-1.5. The sample also shows an increase in [S/Mg] with [Fe/H], most probably because of enrichment from Type Ia supernovae.