  In this paper, we study the evolutions of a self-gravitating cloud of bosonic
dark matter with finite angular momentum and self-interaction. This is achieved
by using the sixth-order pseudospectral operator splitting method to solve the
system of nonlinear Schr\"odinger and Poisson equations. The initial cloud is
assumed to have mass density randomly distributed throughout three-dimensional
space. The dark matter particles in the initial cloud are in the kinetic
regime, i.e., their de Broglie wavelength is much smaller than the halo size.
  It is shown that Bose stars are indeed formed in the numerical simulation
presented here. The presence of angular momentum and self-interaction in the
initial cloud can significantly influence the star formation time in a
non-trivial fashion. Furthermore, the plots of the vorticity magnitude profile
after the star formation time indicate that the formed star may not have any
intrinsic angular momentum for the cases when the self-interaction among the
particles is either negligible or attractive. These results are in agreement
with the earlier analytical studies of an isolated rotating Bose star. However,
for the case of repulsive self-interaction, the vorticity magnitude analysis
shows a possibility that the star formed in the numerical simulations may
possess intrinsic angular momentum. It is also shown that the average mass and
radius diagrams of the star are strongly influenced by the presence of angular
momentum in the initial cloud.
