/ AbstractHigh-energy cosmic rays that hit the Earth can be used to study large-scale atmospheric perturbations. After a first interaction in the upper parts of the atmosphere, cosmic rays produce a shower of particles that sample the atmosphere down to the detector level. The HAWC (High-Altitude Water Cherenkov) cosmic-ray observatory in Central Mexico at 4,100 m elevation detects air shower particles continuously with 300 water Cherenkov detectors with an active area of 12,500 m$^{2}$. On January 15th, 2022, HAWC detected the passage of the pressure wave created by the explosion of the Hunga volcano in the Tonga islands, 9,000 km away, as an anomaly in the measured rate of shower particles. The HAWC measurements are used to characterize the shape of four pressure wave passages, determine the propagation speed of each one, and correlate the variations of the shower particle rates with the barometric pressure changes, extracting a barometric parameter. The profile of the shower particle rate and atmospheric pressure variations for the first transit of the pressure wave at HAWC is compared to the pressure measurements at Tonga island, near the volcanic explosion. This work opens the possibility of using large particle cosmic-ray air shower detectors to trace large atmospheric transient waves.