We propose coupling two internal atomic states using a pair of Raman beams operated in Laguerre-Gaussian laser modes with unequal phase windings. This generates a coupling between the atom's pseudospin and its orbital angular momentum. We analyze the single-particle properties of the system using realistic parameters and provide detailed studies of the spin texture of the ground state. Finally, we consider a weakly interacting atomic condensate subject to this angular spin-orbit coupling and show how the interatomic interactions modify the single-particle physics.