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The spin of intergalactic filaments has been predicted from simulations, and supported by tentative evidence from redshift-space filament shapes in a galaxy redshift survey: generally, a filament is redshifted on one side of its axis, and blueshifted on the other. Here, we investigate whether filament spins could have a measurable kinetic Sunyaev-Zel'dovich (kSZ) signal, from CMB photons being scattered by moving ionised gas; this pure velocity information is complementary to filament redshift-space shapes. We propose to measure the kSZ dipole by combining galaxy redshift surveys with CMB experiments. We base our S/N analyses first on an existing filament catalogue, and its combination with Planck data. We then investigate the detectability of the kSZ dipole using the combination of DESI or SKA-2 with next-stage CMB experiments. We find that the gas halos of filament galaxies co-rotating with filaments induce a stronger kSZ dipole signal than that from the diffuse filamentary gas, but both signals seem too small to be detected in near-term surveys such as DESI+future CMB experiments. But the combination of SKA-2 with future CMB experiments could give a more than 10$σ$ detection. The gain comes mainly from an increased area overlap and an increased number of filaments, but also the low noise and high resolution in future CMB experiments are important to capture signals from filaments small on the sky. Successful detection of the signals may help to find the gravitomagnetic effect in large-scale structure and advance our understanding of baryons in the cosmic web.