  We demonstrate a scheme for optical cycling in the polar, diatomic molecule
strontium monofluoride (SrF) using the $X ^2\Sigma^+\toA^2\Pi_{1/2}$ electronic
transition. SrF's highly diagonal Franck-Condon factors suppress vibrational
branching. We eliminate rotational branching by employing a quasi-cycling
$N=1\to N^\prime=0$ type transition in conjunction with magnetic field remixing
of dark Zeeman sublevels. We observe cycling fluorescence and deflection
through radiative force of an SrF molecular beam using this scheme. With
straightforward improvements our scheme promises to allow more than $10^5$
photon scatters, possibly enabling the direct laser cooling of SrF.
