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We perform a direct search for an isotropic stochastic gravitational-wave background (SGWB) produced by cosmic strings in the Parkes Pulsar Timing Array (PPTA) Data Release 2 (DR2). We find no evidence for such an SGWB, and therefore place a 95% confidence level upper limit on the cosmic string tension, G μ , as a function of the reconnection probability, p , which can be less than 1 in the string-theory-inspired models or pure Yang–Mills theory. The upper bound on the cosmic string tension is G μ ≲ 5.1 × 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 bursts from cosmic string cusps in the PPTA DR2, and comparable to previous bounds derived from the null search of the SGWB from cosmic strings.