  We determine the effective $g$-factor ($|g^\ast|$) of a two-dimensional
electron gas (2DEG) using a new method based on capacitance spectroscopy. The
capacitance-voltage profile of a 2DEG in an InAs/AlGaSb quantum well measured
in an in-plane magnetic field shows a double-step feature that indicates the
Zeeman splitting of the subband edge. The method allows for simultaneous and
independent determination of $|g^\ast|$ and effective mass $m^\ast$. Data
suggest that the biaxial tensile strain in the InAs layer has considerable
impacts on both $m^\ast$ and $g^\ast$. Our method provides a means to determine
$|g^\ast|$ that is complementary to the commonly used coincidence technique.
