  We present rules for computing scattering amplitudes of charged scalar matter
and photons, where the photon has non-zero spin Casimir $\rho$, and is
therefore a continuous spin particle (CSP). The amplitudes reduce to familiar
scalar QED when $\rho\rightarrow 0$. As a concrete example, we compute the pair
annihilation and Compton scattering amplitudes in this theory and comment on
their physical properties, including unitarity and scaling behavior at small
and large $\rho$.
