Search for the radiative decay <i>D</i><SUP>+</SUP><i>_s</i> → γρ(770)<SUP>+</SUP>

Using 7.33 fb(-1) of e(+)e(-) collision data samples collected with the BESIII detector at center-of-mass energies between 4.128 and 4.226 GeV, we search for the radiative decay D-s(+)-> gamma rho(770)(+) for the first time. A hint of D-s(+) -> gamma rho(770)(+) is observed with a statistical significance of 2.5 sigma. The branching fraction of D-s(+) -> gamma rho(770)(+) is measured to be (2.2 +/- 0.9(stat.) +/- 0.2(syst.)) x 10(-4), corresponding to an upper limit of 6.1 x 10(-4) at the 90% confidence level.