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We use a single trapped ^40 Ca ^+ ion as a resonant, polarization-sensitive absorber to detect and characterize the entanglement of tunable narrowband photon pairs from a spontaneous parametric down-conversion source. Single-photon absorption is marked by a quantum jump in the ion and heralded by coincident detection of the partner photon. For three polarization basis settings of the absorption and detection of the herald, we find maximum coincidences always for orthogonal polarizations. The polarization entanglement is further evidenced by tomographic reconstruction of the biphoton quantum state with an overlap fidelity of 93% with the Bell singlet state. This is an essential step toward a single-ion based quantum memory for photonic entanglement.