  We analyze the C4 catalog of galaxy clusters from the Sloan Digital Sky
Survey (SDSS) to investigate the axis-ratio distribution of the projected two
dimensional cluster profiles. We consider only those objects in the catalog
whose virial mass is close to 10^{14}h^{-1}M_{sun}, with member galaxies within
the scale radius 1000 kpc. The total number of such objects turns out to be
336. We also derive a theoretical distribution by incorporating the effect of
projection onto the sky into the analytic formalism proposed recently by Lee,
Jing, & Suto. The theoretical distribution of the cluster axis-ratios is shown
to depend on the amplitude of the linear power spectrum (sigma_8) as well as
the density parameter (Omega_{m}). Finally, fitting the observational data to
the analytic distribution with Omega_{m} and sigma_{8} as two adjustable free
parameters, we find the best-fitting value of sigma_{8}=(1.01 +/-
0.09)(Omega_{m}/0.6)^{(0.07 +/- 0.02) +0.1 Omega_{m}}$. It is a new
sigma_{8}-Omega_{m} relation, different from the previous one derived from the
local abundance of X-ray clusters. We expect that the axis-ratio distribution
of galaxy clusters, if combined with the local abundance of clusters, may put
simultaneous constraints on sigma_{8} and Omega_{m}.
