The observational signatures of black holes in x-ray binary systems depend on their masses, spins, accretion rate, and the misalignment angle between the black hole spin and the orbital angular momentum. We present optical polarimetric observations of the black hole x-ray binary MAXI J1820+070, from which we constrain the position angle of the binary orbital. Combining this with previous determinations of the relativistic jet orientation, which traces the black hole spin, and the inclination of the orbit, we determine a lower limit of 40° on the spin-orbit misalignment angle. The misalignment must originate from either the binary evolution or black hole formation stages. If other x-ray binaries have similarly large misalignments, these would bias measurements of black hole masses and spins from x-ray observations.