We made observations of magnetic field variations in association with pulsating auroras with the magneto‐impedance sensor magnetometer (MIM) carried by the Loss through Auroral Microburst Pulsations (LAMP) sounding rocket that was launched at 11:27:30 UT on 5 March 2022 from Poker Flat Research Range, Alaska. At an altitude of 200–250 km, MIM detected clear enhancements of the magnetic field by 15–25 nT in both the northward and westward components. From simultaneous observations with the ground all‐sky camera, we found that the footprint of LAMP at the 100 km altitude was located near the center of a pulsating auroral patch. The auroral patch had a dimension of ∼90 km in latitude and ∼25 km in longitude, and its major axis was inclined toward northwest. These observations were compared with results of a simple model calculation, in which local electron precipitation into the thin‐layer ionosphere causes an elliptical auroral patch. The conductivity within the patch is enhanced in the background electric field and as a result, the magnetic field variations are induced around the auroral patch. The model calculation results can explain the MIM observations if the electric field points toward southeast and one of the model parameters is adjusted. We conclude that the pulsating auroral patch in this event was associated with a one‐pair field‐aligned current that consists of downward (upward) currents at the poleward (equatorward) edge of the patch. This current structure is maintained even if the auroral patch is latitudinally elongated. Key Points Magneto‐impedance (MI) sensor was carried by a sounding rocket and first applied to magnetic field measurement in space Magnetic field variations were observed when the footprint of the payload was located near the center of an auroral patch The magnetic field variations are thought to be caused by field‐aligned currents flowing at the edges of the pulsating auroral patch