Photons are one of the prominent candidates for long-distance quantum communication and quantum information processing. Certain quantum information processing tasks require storage and faithful retrieval of single photons preserving the internal states of the photons. Here we propose a method to store the vector-vortex states of light in the intra-atomic frequency comb based quantum memory. We show that an atomic ensemble with two intra-atomic frequency combs corresponding to $\Delta m = \pm1$ transitions of similar frequency are sufficient for a robust and efficient quantum memory for vector-vortex states of light. As an example, we show that the Cs and Rb atoms are good candidates for storing these internal modes of light.