  Matter-wave interferometers are, in principle, orders of magnitude more
sensitive than their optical counterparts. Nevertheless, creation of
matter-wave currents to achieve such a sensitivity is a continuing challenge.
Here, we propose the use of Optical Angular Momentum (OAM) induced vortex
superpositions in Bose-Einstein Condensates (BECs) as an alternative to atom
interferometers for gyroscopy. The coherent superposition of two
counter-rotating vortex states of a trapped condensate leads to an interference
pattern that rotates by an angle proportional to the angular velocity of the
rotating trap \mdash in accordance with the Sagnac effect. We show that the
rotation rate can be easily read out and that the device is highly stable. The
signal-to-noise ratio and sensitivity of the scheme are also discussed.
