The angular momentum comes from the chaotic/turbulent collapse of the parent molecular cloud. The collapse is turbulent because the initial conditions in the parent cloud are not spherically symmetric. This leave the proto-stellar clumps with non-zero angular momentum even if the parent cloud started with zero angular momentum. The sum of the angular momenta of all the material of the original cloud after fragmentation is still that of the cloud before fragmentation.
Some other/external triggering events for molecular cloud collapse can impart non-zero angular momentum to the cloud as a whole, but this is not necessary for the the individual fragments to end up with angular momentum.
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