  We consider random permutations derived by sampling from stick-breaking
partitions of the unit interval. The cycle structure of such a permutation can
be associated with the path of a decreasing Markov chain on $n$ integers. Under
certain assumptions on the stick-breaking factor we prove a central limit
theorem for the logarithm of the order of the permutation, thus extending the
classical Erd\H{o}s-Tur\'an law for the uniform permutations and its
generalization for Ewens' permutations associated with sampling from the
PD/GEM$(\theta)$ distribution. Our approach is based on using perturbed random
walks to obtain the limit laws for the sum of logarithms of the cycle lengths.
