  The existence and dynamics of stable quantized vortices is an important
subject of quantum many-body physics. Spin-orbital-angular-momentum coupling
(SOAMC), a special type of spin-orbit coupling, has been experimentally
achieved to create vortices in atomic Bose-Einstein condensates (BEC). Here, we
generalize the concept of SOAMC to a two-component polariton BEC and analyze
the emergence and configuration of vortices under a finite-size circular
pumping beam. We find that the regular configuration of vortex lattices induced
by a finite-size circular pump is significantly distorted by the spatially
dependent Raman coupling of SOAMC, even in the presence of a repulsive
polariton interaction which can assist the forming of stable vortex
configuration. Meanwhile, a pair of vortices induced by SOAMC located at the
center of polariton cloud remains stable. When the Raman coupling is
sufficiently strong and interaction is weak, the vortices spiraling in from the
edge of polariton cloud will disrupt the polariton BEC.
