We report the first detection of the X-ray polarization of the bright transient Swift J1727.8−1613 with the Imaging X-ray Polarimetry Explorer. The observation was performed at the beginning of the 2023 discovery outburst, when the source resided in the bright hard state. We find a time- and energy-averaged polarization degree of 4.1% ± 0.2% and a polarization angle of 22 ± 13 (errors at 68% confidence level; this translates to ∼20σ significance of the polarization detection). This finding suggests that the hot corona emitting the bulk of the detected X-rays is elongated, rather than spherical. The X-ray polarization angle is consistent with that found in submillimeter wavelengths. Since the submillimeter polarization was found to be aligned with the jet direction in other X-ray binaries, this indicates that the corona is elongated orthogonal to the jet.