  The formation of $^{40}$Ca$_2^+$ molecular ions is observed in a hybrid
$^{40}$Ca magneto-optical and ion trap system. The molecular ion formation
process is determined to be two-photon photo-associative ionization of
ultracold $^{40}$Ca atoms. A lower bound for the two-body, two-photon rate
constant is found to be $\bar{\beta} \geq 2 \pm 1 \times 10^{-15}$ cm$^{3}$ Hz.
$\textit{Ab initio}$ molecular potential curves are calculated for the neutral
Ca$_2$ and ionic Ca$_2^+$ molecules and used in a model that identifies the
photo-associative ionization pathway. As this technique does not require a
separate photo-association laser, it could find use as a simple, robust method
for producing ultracold, state-selected molecular ions.
