  We present theoretical predictions for photometric and spectroscopic
signatures of rings around transiting extrasolar planets. On the basis of a
general formulation for the transiting signature in the stellar light curve and
the velocity anomaly due to the Rossiter effect, we compute the expected
signals analytically for a face-on ring system, and numerically for more
general configurations. We study the detectability of a ring around a
transiting planet located at a=3AU for a variety of obliquity and azimuthal
angles, and find that it is possible to detect the ring signature both
photometrically and spectroscopically unless the ring is almost edge-on (i.e.,
the obliquity angle of the ring \theta is much less than unity). We also
consider the detectability of planetary rings around a close-in planet, HD
209458b ($\theta\approx 90^\circ-i_{\rm orbit} \approx 3^\circ.32$), and Saturn
($\theta \approx 26^\circ.7$) as illustrative examples. While the former is
difficult to detect with the current precision (photometric precision of 10^-4
and radial velocity precision of 1 m/s), a marginal detection of the latter is
possible photometrically. If the future precision of the radial velocity
measurement reaches even below 0.1 m/s, they will be even detectable from the
ground-based spectroscopic observations.
