ABSTRACT We explore a sample of 1492 galaxies with measurements of the mean stellar population properties and the spin parameter proxy, $\lambda _{R_{\rm {e}}}$, drawn from the SAMI Galaxy Survey. We fit a global $\alpha /\rm {Fe}$–σ relation, finding that ${\alpha /\rm {Fe}}=(0.395\pm 0.010)\rm {log}_{10}(\sigma)-(0.627\pm 0.002)$. We observe an anti-correlation between the residuals $\Delta \alpha /\rm {Fe}$ and the inclination-corrected $\lambda _{\, R_{\rm {e}}}^{\rm {\, eo}}$, which can be expressed as ${\Delta \alpha /\rm {Fe}}=(-0.057\pm 0.008){\lambda _{\, R_{\rm {e}}}^{\rm {\, eo}}}+(0.020\pm 0.003)$. The anti-correlation appears to be driven by star-forming galaxies, with a gradient of ${\Delta \alpha /\rm {Fe}}\sim (-0.121\pm 0.015){\lambda _{\, R_{\rm {e}}}^{\rm {\, eo}}}$, although a weak relationship persists for the subsample of galaxies for which star formation has been quenched. We take this to be confirmation that disc-dominated galaxies have an extended duration of star formation. At a reference velocity dispersion of 200 km s−1, we estimate an increase in half-mass formation time from ∼0.5 Gyr to ∼1.2 Gyr from low- to high-$\lambda _{\, R_{\rm {e}}}^{\rm {\, eo}}$ galaxies. Slow rotators do not appear to fit these trends. Their residual α-enhancement is indistinguishable from other galaxies with ${\lambda _{\, R_{\rm {e}}}^{\rm {\, eo}}}\lessapprox 0.4$, despite being both larger and more massive. This result shows that galaxies with ${\lambda _{\, R_{\rm {e}}}^{\rm {\, eo}}}\lessapprox 0.4$ experience a similar range of star formation histories, despite their different physical structure and angular momentum.