The surface of W(110) exhibits a spin-orbit-induced Dirac-cone-like surface state, which is of mainly d_z² orbital character near [(Γ)], although it is strongly influenced by the twofold C_2v surface symmetry. Its distinctive k-dependent spin polarization along [(Γ)] [(H)] is revealed by spin- and angle-resolved photoemission excited with p-and s-polarized light. The spin texture of the surface state is found to change sign upon switching from p- to s-polarized light. Based on electronic-structure calculations, this behavior is explained by the orbital composition of the Dirac-cone-like state. The dominant part of the state has even mirror symmetry and is excited by p-polarized light. A minor part with odd symmetry is excited by s-polarized light and exhibits a reversed spin polarization. Our study demonstrates in which way spin-orbit interaction combines the spin degree of freedom with the orbital degree of freedom and opens a way to manipulate the spin information gathered from the Dirac-cone-like surface state by light. Our results prove that "spin control" is not restricted to topological surface states with p-type orbital symmetry in topological insulators.