The ordinary Hall effect refers to generation of a transverse voltage upon exertion of an electric field in the presence of an out-of-plane magnetic field. While a linear Hall effect is commonly observed in systems with breaking time-reversal symmetry via an applied external magnetic field or their intrinsic magnetization1, 2, a nonlinear Hall effect can generically occur in non-magnetic systems associated with a nonvanishing Berry curvature dipole3. Here we report, observations of a nonlinear optical Hall effect in a Weyl semimetal WTe2 without an applied magnetic field at room temperature. We observe an optical Hall effect resulting in a polarization rotation of the reflected light, referred to as the nonlinear Kerr rotation. The nonlinear Kerr rotation linearly depends on the charge current and optical power, which manifests the fourth-order nonlinearity. We quantitatively determine the fourth-order susceptibility, which exhibits strong anisotropy depending on the directions of the charge current and the light polarization. Employing symmetry analysis of Berry curvature multipoles, we demonstrate that the nonlinear Kerr rotations can arise from the Berry curvature hexapole allowed by the crystalline symmetries of WTe2. There also exist marginal signals that are incompatible with the symmetries, which suggest a hidden phase associated with the nonlinear process.