ABSTRACT We simulate star formation in two molecular clouds extracted from a larger disc-galaxy simulation with a spatial resolution of ∼0.1 pc, one exiting a spiral arm dominated by compression, and another in an inter-arm region more strongly affected by galactic shear. Treating the stars as ‘sink particles’, we track their birth angular momentum, and the later evolution of their angular momentum due to gas accretion. We find that in both clouds, the sinks have spin vectors that are aligned with one another, and with the global angular momentum vector of the star cluster. This alignment is present at birth, but enhanced by later gas accretion. In the compressive cloud, the sink-spins remain aligned with the gas for at least a free-fall time. By contrast, in the shear cloud, the increased turbulent mixing causes the sinks to rapidly misalign with their birth cloud on approximately a gas free-fall time. In spite of this, both clouds show a strong alignment of sink-spins at the end of our simulations, independently of environment.