  We study muon pair production $ e^+ e^- \to \mu^+ \mu^-$ in the
noncommutative(NC) extension of the standard model using the Seiberg-Witten
maps of this to the second order of the noncommutative parameter $\Theta_{\mu
\nu}$. Using $\mathcal{O}(\Theta^2)$ Feynman rules, we find the
$\mathcal{O}(\Theta^4)$ cross section(with all other lower order contributions
simply cancelled) for the pair production. The momentum dependent
$\mathcal{O}(\Theta^2)$ NC interaction significantly modifies the cross section
and angular distributions which are different from the commuting standard
model. We study the collider signatures of the space-time noncommutativity at
the International Linear Collider(ILC) and find that the process $ e^+ e^- \to
\mu^+ \mu^-$ can probe the NC scale $\Lambda$ in the range $0.8 - 1.0$ TeV for
typical ILC energy ranges.
