TOI-640 b is a hot, puffy Jupiter with a mass of 0.57 ± 0.02 MJ and radius of 1.72 ± 0.05 RJ, orbiting a slightly evolved F-type star with a separation of 6.33−0.06+0.07 R⋆. 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 λ = 184 ± 3°. From the TESS light curve, we measured the stellar rotation period, allowing us to determine the stellar inclination, i⋆ = 23−2+3°, meaning we are viewing the star pole-on. Combining this with the orbital inclination allowed us to calculate the host star obliquity, ψ = 104 ± 2°. TOI-640 b joins a group of planets orbiting over stellar poles within the range 80°–125°. The origin of this orbital configuration is not well understood.