  We have completed a measurement of the Stark shift within the $^{115}$In
$6s_{1/2} \rightarrow 6p_{1/2}$ excited-state transition using two-step laser
spectroscopy in an indium atomic beam. Combining this measurement with recent
experimental results we determine the scalar polarizability, $\alpha_{0}$, of
the $6p_{1/2}$ state to be $7683 \pm43 \,a_{0}^{3}$ in atomic units, a result
which agrees very well with recent theoretical calculations. In this
experiment, one laser, stabilized to the $5p_{1/2} \rightarrow 6s_{1/2}$ 410~nm
transition, was directed transversely to the atomic beam, while a second,
overlapping laser was scanned across the 1343~nm $6s_{1/2} \rightarrow
6p_{1/2}$ transition. We utilized two-tone frequency-modulation spectroscopy of
the infrared laser beam to measure the second-step absorption in the
interaction region, where the optical depth is less than 10$^{-3}$. In the
course of our experimental work we also determined the hyperfine splitting
within the $6p_{1/2}$ state, improving upon the precision of an existing
measurement.
