  We describe a novel twistorial construction of the asymptotic BMS symmetries
at null infinity for asymptotically flat spacetimes. We define BMS twistors as
spinor solutions to some set of components of the usual spacetime twistor
equation restricted to null infinity. The space of BMS twistors is
infinite-dimensional. We show that given two BMS twistors their symmetric
tensor product can be used to generate (complex) vector fields which are the
infinitesimal BMS symmetries of null infinity. In this sense BMS twistors are
"square roots" of BMS symmetries. We also show that these BMS twistor equations
can be written a pair of covariant spinor-valued equations which are completely
determined by the intrinsic universal structure of null infinity.
