We demonstrate multiple photon cycling and radiative force deflection on the triatomic free radical strontium monohydroxide (SrOH). Optical cycling is achieved on SrOH in a cryogenic buffer-gas beam by employing the rotationally closed $P(N’’ = 1)$ branch of the vibronic transition ${\tilde{X}}^{2}{{\rm{\Sigma }}}^{+}(000)\leftrightarrow {\tilde{A}}^{2}{{\rm{\Pi_{1 / 2} }}} (000)$. A single repumping laser excites the Sr–O stretching vibrational mode, and photon cycling of the molecule deflects the SrOH beam by an angle of $0.2^\circ $ via scattering of $\sim 100$ photons per molecule. This approach can be used for direct laser cooling of SrOH and more complex, isoelectronic species.