Bulk diamond phonons have been shown to be a versatile platform for the generation, storage, and manipulation of high-bandwidth quantum states of light. Here we demonstrate a diamond quantum memory that stores, and releases on demand, an arbitrarily polarized $sim$250 fs duration photonic qubit. The single-mode nature of the memory is overcome by mapping the two degrees of polarization of the qubit, via Raman transitions, onto two spatially distinct optical phonon modes located in the same diamond crystal. The two modes are coherently recombined upon retrieval and quantum process tomography confirms that the memory faithfully reproduces the input state with average fidelity $0.784pm0.004$ with a total memory efficiency of $(0.76pm0.03)%$. In an additional demonstration, one photon of a polarization-entangled pair is stored in the memory. We report that entanglement persists in the retrieved state for up to 1.3 ps of storage time. These results demonstrate that the diamond phonon platform can be used in concert with polarization qubits, a key requirement for polarization-encoded photonic processing.