  Recently we have demonstrated that high-precision polarization observations
can detect the polarization resulting from the rotational distortion of a
rapidly rotating B-type star. Here we investigate the extension of this
approach to an A-type star. Linear-polarization observations of $\alpha$ Oph
(A5IV) have been obtained over wavelengths from 400 to 750 nm. They show the
wavelength dependence expected for a rapidly-rotating star combined with a
contribution from interstellar polarization. We model the observations by
fitting rotating-star polarization models and adding additional constraints
including a measured $v_e \sin{i}$. However, we cannot fully separate the
effects of rotation rate and inclination, leaving a range of possible
solutions. We determine a rotation rate $\omega = \Omega/\Omega_ c$ between
0.83 and 0.98 and an axial inclination i > 60 deg. The rotation-axis position
angle is found to be 142 $\pm$ 4 deg, differing by 16 deg from a value obtained
by interferometry. This might be due to precession of the rotation axis due to
interaction with the binary companion. Other parameters resulting from the
analysis include a polar temperature Tp = 8725 $\pm$ 175 K, polar gravity
$\log{g_p} = 3.93 \pm 0.08$ (dex cgs), and polar radius $R_{\rm p} = 2.52 \pm
0.06$ Rsun. Comparison with rotating-star evolutionary models indicates that
$\alpha$ Oph is in the later half of its main-sequence evolution and must have
had an initial $\omega$ of 0.8 or greater. The interstellar polarization has a
maximum value at a wavelength ($\lambda_{\rm max}$) of $440 \pm 110$ nm,
consistent with values found for other nearby stars.
