  We perform a direct search for an isotropic stochastic gravitational-wave
background (SGWB) produced by cosmic strings in the Parkes Pulsar Timing Array
second data release. We find no evidence for such an SGWB, and therefore place
$95\%$ confidence level upper limits on the cosmic string tension, $G\mu$, as a
function of the reconnection probability, $p$, which can be less than 1 in the
string-theory-inspired models. The upper bound on the cosmic string tension is
$G\mu \lesssim 5.1 \times 10^{-10}$ for $p = 1$, which is about five orders of
magnitude tighter than the bound derived from the null search of individual
gravitational wave burst from cosmic string cusps in the PPTA DR2.
