  In this article, we investigate the stationary, soliton-like solutions in the
model of the Einstein gravity coupled to a free and complex scalar field, and
extend chains of mini-boson stars to the rotating case. These solutions
manifest as multiple rotating mini-boson stars uniformly arranged along the
rotation axis. Through numerical methods, we obtain chains of rotating
mini-boson stars with one to five constituents. We show the distribution of the
field functions for these chain solutions. Additionally, we also study the
effect of the frequency of the complex scalar field on the ADM mass $M$ and
angular momentum $J$. By comparing the conclusions of the rotating case with
the non-rotating case, there are some intriguing differences. Furthermore, we
observe that there exist two ergospheres for some of these solutions.
