  We present a quantitative analysis of the time-delay effect on the cosmic
background radiation (CBR) by static gravitational potential of galaxy
clusters. This is primarily motivated by growing observational evidence that
clusters have essentially experienced no-evolution since redshift $z\approx1$,
indicating that the contribution of a time-dependent potential to CBR
anisotropy discussed in literature could be rather small for the
dynamically-relaxed clusters. Using the softened isothermal sphere model and
the universal density profile for the mass distribution of rich clusters, we
calculate the CBR anisotropy by the time-delay effect and compare it with those
generated by the thermal and kinematic S-Z effects as well as by the transverse
motion of clusters. While it is unlikely that the time-delay effect is
detectable in the current S-Z measurement because of its small amplitude of
$10^{-6}$-$10^{-7}$ and its achromaticity, it nevertheless leads to an
uncertainty of $\sim10%$ in the measurement of the kinematic S-Z effect of
clusters. Future cosmological application of the peculiar velocity of clusters
to be measured through the S-Z effect should therefore take this uncertainty
into account.
