TOI-640 b is a hot, puffy Jupiter with a mass of $0.57 \pm 0.02$ M$_{\rm J}$ and radius of $1.72 \pm 0.05$ R$_{\rm J}$, orbiting a slightly evolved F-type star with a separation of $6.33^{+0.07}_{-0.06}$ R$_\star$. Through spectroscopic in-transit observations made with the HARPS spectrograph, we measured the Rossiter-McLaughlin effect, analysing both in-transit radial velocities and the distortion of the stellar spectral lines. From these observations, we find the host star to have a projected obliquity of $\lambda=184\pm3^\circ$. From the TESS light curve, we measured the stellar rotation period, allowing us to determine the stellar inclination, $i_\star=23^{+3\circ}_{-2}$, meaning we are viewing the star pole-on. Combining this with the orbital inclination allowed us to calculate the host star obliquity, $\psi=104\pm2^\circ$. TOI-640 b joins a group of planets orbiting over stellar poles within the range $80^\circ-125^\circ$. The origin of this orbital configuration is not well understood.