  In a previous paper, using an equation of state of dense matter representing
a fluid of Skyrmions we constructed the corresponding non-rotating compact-star
models in hydrostatic equilibrium; these are mostly fluid stars (the Skyrmion
fluid) thus naming them {\it Skyrmion Stars}.
  Here we generalize our previous calculations by constructing equilibrium
sequences of rotating Skyrmion stars in general relativity using the computer
code {\it RNS} developed by Stergioulas. We calculated their masses and radii
to be 0.4 \le M/M_{\odot} \le 3.45, and 13.0 {\rm km}\le R\le 23.0 {\rm km},
respectively (R being the circumferential radius of the star). The period of
the maximally rotating Skyrmion stars is calculated to be 0.8 {\rm ms}\le P \le
2.0 {\rm ms}. We find that a gap (the height between the star surface and the
inner stable circular orbit) starts to appear for M\sim 2.0M_{\odot}.
Specifically, the Skyrmion star mass range with an existing gap is calculated
to be 1.8 < M/ M_{\odot} < 3.0 with the corresponding orbital frequency 0.8
{\rm kHz} < \nu_{\rm ISCO} < 1.3 {\rm kHz}. We apply our model to the 4U
1820-30 low mass X-ray binary and suggest a plausible Skyrmion star candidate
in the 4U 1636-53 system. We discuss the difficulties encountered by our model
in the 4U 0614+09 case with the highest known Quasi-Periodic Oscillation
frequency of 1329 Hz. A comparative study of Skyrmion stars and models of
neutron stars based on recent/modern equations of state is also presented.
