Magnetic flux quantization is one of the defining properties of a superconductor. We report the observation of half-integer magnetic flux quantization in mesoscopic rings of superconducting beta-Bi2Pd thin films. The half-quantum fluxoid manifests itself as a pi phase shift in the quantum oscillation of the superconducting critical temperature. This result verifies unconventional superconductivity of beta-Bi2Pd and is consistent with a spin-triplet pairing symmetry. Our findings may have implications for flux quantum bits in the context of quantum computing.