  Stellar clusters form by gravitational collapse of turbulent molecular
clouds, with up to several thousand stars per cluster. They are thought to be
the birthplace of most stars and therefore play an important role in our
understanding of star formation, a fundamental problem in astrophysics. The
initial conditions of the molecular cloud establish its dynamical history until
the stellar cluster is born. However, the evolution of the cloud's angular
momentum during cluster formation is not well understood. Current observations
have suggested that turbulence scrambles the angular momentum of the
cluster-forming cloud, preventing spin alignment amongst stars within a
cluster. Here we use asteroseismology to measure the inclination angles of spin
axes in 48 stars from the two old open clusters NGC~6791 and NGC~6819. The
stars within each cluster show strong alignment. Three-dimensional
hydrodynamical simulations of proto-cluster formation show that at least 50 %
of the initial proto-cluster kinetic energy has to be rotational in order to
obtain strong stellar-spin alignment within a cluster. Our result indicates
that the global angular momentum of the cluster-forming clouds was efficiently
transferred to each star and that its imprint has survived after several
gigayears since the clusters formed.
