A prime category of superconducting materials in which to look for spin-triplet pairing and topological superconductivity are superconductors without inversion symmetry. It is predicted that the breaking of parity symmetry gives rise to an admixture of spin-singlet / spin-triplet pairing states; a triplet pairing component, being substantial, seems all but guaranteed. However, the experimental confirmation of pair mixing in any particular material remains elusive. In this work, we perform phase-sensitive experiment to examine the pairing state of noncentrosymmetric superconductor $alpha-$BiPd. The Little-Parks effect observed in mesoscopic polycrystalline $alpha-$BiPd ring devices reveals the presence of half-integer magnetic flux quantization, which provides a decisive evidence for the spin-triplet pairing state. We find mixed half-quantum fluxes and integer-quantum fluxes, consistent with the scenario of singlet-triplet pair mixing.