  We study the production cross section of the $t$-channel single top quark at
the LHC in the noncommutative space-time. It is shown that the deviation of the
$t$-channel single top cross section from the Standard Model value because of
noncommutativity is significant when $|\vec{\theta}| \gtrsim 10^{-4}$
GeV$^{-2}$. Using the present experimental precision in measurement of the
$t$-channel cross section, we apply upper limit on the noncommutative
parameter. When a single top quark decays, there is a significant amount of
angular correlation, in the top quark rest frame between the top spin direction
and the direction of the charged lepton momentum from its decay. We study the
effect of noncommutativity on the spin correlation and we find that depending
on the noncommutative scale, the angular correlation can enhance considerably.
Then, we provide limits on the noncommutative scale for various possible
relative uncertainties on the spin correlation measurement.
