Aims. We present the first measurements of the angular-momentum flux in the solar wind recorded by the Solar Orbiter spacecraft. Our aim is to validate these measurements to support future studies of the Sun’s angular-momentum loss. Methods. We combined 60-min averages of the proton bulk moments and the magnetic field measured by the Solar Wind Analyser and the magnetometer onboard Solar Orbiter. We calculated the angular-momentum flux per solid-angle element using data from the first orbit of the mission’s cruise phase in 2020. We separated the contributions from protons and from magnetic stresses to the total angular-momentum flux. Results. The angular-momentum flux varies significantly over time. The particle contribution typically domin...