The decay $Z_c(3900)^\pm\to\omega\pi^\pm$ is searched for using data samples
collected with the BESIII detector operating at the BEPCII storage ring at
center-of-mass energies $\sqrt{s}=4.23$ and $4.26$~GeV. No significant signal
for the $Z_c(3900)^\pm$ is found, and upper limits at the 90\% confidence level
on the Born cross section for the process $e^+e^-\to
Z_c(3900)^\pm\pi^\mp\to\omega\pi^+\pi^-$ are determined to be $0.26$ and $0.18$
pb at $\sqrt{s}=4.23$ and 4.26 GeV, respectively.
