  An experimental proposal for realizing spin-orbit (SO) coupling of
pseudospin-1 in the ground manifold $^1\Sigma(\upsilon=0)$ of (bosonic)
bialkali polar molecules is presented. The three spin components are composed
of the ground rotational state and two substates from the first excited
rotational level. Using hyperfine resolved Raman processes through two select
excited states resonantly coupled by a microwave, an effective coupling between
the spin tensor and linear momentum is realized. The properties of
Bose-Einstein condensates for such SO-coupled molecules exhibiting dipolar
interactions are further explored. In addition to the SO-coupling-induced
stripe structures, the singly and doubly quantized vortex phases are found to
appear, implicating exciting opportunities for exploring novel quantum physics
using SO-coupled rotating polar molecules with dipolar interactions.
