  The 4-dimensional model of a massless particle with rigidity whose Lagrangian
is proportional to its world-line curvature is reformulated in terms of spinor
and twistor variables. We begin with a first-order Lagrangian that is
equivalent to the original Lagrangian proportional to the extrinsic curvature
of a particle world-line. The first-order Lagrangian is written in terms of
spacetime and spinor variables, leading to a spinor representation of the
Lagrangian. Then its corresponding action is expressed in terms of twistor
variables, leading to the gauged Shirafuji action.
