  Aims: We present the first measurements of the solar-wind angular-momentum
(AM) flux recorded by the Solar Orbiter spacecraft. Our aim is the validation
of these measurements to support future studies of the Sun's AM loss. Methods:
We combine 60-minute averages of the proton bulk moments and the magnetic field
measured by the Solar Wind Analyser (SWA) and the magnetometer (MAG) onboard
Solar Orbiter. We calculate the AM flux per solid-angle element using data from
the first orbit of the mission's cruise phase during 2020. We separate the
contributions from protons and from magnetic stresses to the total AM flux.
Results: The AM flux varies significantly over time. The particle contribution
typically dominates over the magnetic-field contribution during our measurement
interval. The total AM flux shows the largest variation and is typically
anti-correlated with the radial solar-wind speed. We identify a compression
region, potentially associated with a co-rotating interaction region or a
coronal mass ejection, that leads to a significant localised increase in the AM
flux, yet without a significant increase in the AM per unit mass. We repeat our
analysis using the density estimate from the Radio and Plasma Waves (RPW)
instrument. Using this independent method, we find a decrease in the peaks of
positive AM flux but otherwise consistent results. Conclusions: Our results
largely agree with previous measurements of the solar-wind AM flux in terms of
amplitude, variability, and dependence on radial solar-wind bulk speed. Our
analysis highlights the potential for future, more detailed, studies of the
solar wind's AM and its other large-scale properties with data from Solar
Orbiter. We emphasise the need to study the radial evolution and latitudinal
dependence of the AM flux in combination with data from Parker Solar Probe and
assets at heliocentric distances of 1 au and beyond.
