  General Relativistic calculations in the linear regime have been made for
electromagnetic beams of radiation known as optical vortices. These exotic
beams of light carry a physical quantity known as optical orbital angular
momentum (OAM). It is found that when a massive spinning neutral particle is
placed along the optical axis, a phenomenon known as inertial frame dragging
occurs. Our results are compared with those found previously for a ring laser
and an order of magnitude estimate of the laser intensity needed for a
precession frequency of 1 Hz is given for these "steady" beams of light.
