A black hole x-ray binary (XRB) system forms when gas is stripped from a normal star and accretes onto a black hole, which heats the gas sufficiently to emit x-rays. We report a polarimetric observation of the XRB Cygnus X-1 using the Imaging X-ray Polarimetry Explorer. The electric field position angle aligns with the outflowing jet, indicating that the jet is launched from the inner x-ray-emitting region. The polarization degree is 4.01 ± 0.20% at 2 to 8 kiloelectronvolts, implying that the accretion disk is viewed closer to edge-on than the binary orbit. These observations reveal that hot x-ray-emitting plasma is spatially extended in a plane perpendicular to, not parallel to, the jet axis.