The (pseudo)spin degrees of freedom greatly enriches the physics of cold atoms. This is particularly so for systems with high spins (i.e., spin quantum number larger than 1/2). For example, one can construct not only the rank-1 spin vector, but also the rank-2 spin tensor in high spin systems. Here we propose a simple scheme to couple the spin tensor and the center-of-mass orbital angular momentum in a spin-1 cold atom system and show that this leads to a new quantum phase of the matter: the spin-nematic vortex state that features vorticity in an SU(2) spin-nematic tensor subspace. Under proper conditions, such states are characterized by quantized topological numbers. Our work opens up new avenues of research in topological quantum matter with high spins.