  We report measurements of the ac polarizabilities of ultracold ground-state
$^{23}\rm{Na}^{87}\rm{Rb}$ molecules. While the polarizability of the ground
rotational state $J = 0$ is isotropic, that of the first excited rotational
state $J = 1$ is anisotropic and depends strongly on the light polarization
angle. We obtain both polarizabilities precisely by combining trap oscillation
frequency measurement and high resolution rotational spectroscopy driven by
microwave. With the optimized light polarization angle and intensity
combination, the nonuniformity of the differential ac Stark shift between the
two rotational states is minimized and the rotational coherence time is
observed to be the longest.
