We report on the first experimental realization of the single qubits purification protocol [J. I. Cirac, A. K. Ekert, and C. Macchiavello, Phys. Rev. Lett. 82, 4344 (1999)] for two copies of a qubit sent through a depolarizing channel. The purification of the polarization-encoded photonic qubits is achieved with passive linear optical elements. Our experimental results suggest that the present approach may represent a viable alternative to quantum error correction or entanglement distillation.