The decay $Z_c(3900)^±\toωπ^±$ 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 $Z_c(3900)^±$ is found, and upper limits at the 90\% confidence level on the Born cross section for the process $e^+e^-\to Z_c(3900)^±π^∓\toωπ^+π^-$ are determined to be $0.26$ and $0.18$ pb at $\sqrt{s}=4.23$ and 4.26 GeV, respectively. ; Comment: 7 pages, 3 figures