  We prove that if $\xi$ is a quasisymmetric homeomorphism between Sierpi\'nski
carpets that are the Julia sets of postcritically-finite rational maps, then
$\xi$ is the restriction of a M\"obius transformation to the Julia set. This
implies that the group of quasisymmetric homeomorphisms of a Sierpi\'nski
carpet Julia set of a postcritically-finite rational map is finite.
