Spin-triplet superfluids can support exotic objects, such as half-quantum vortices characterized by the nontrivial winding of the spin structure. We present cantilever magnetometry measurements performed on mesoscopic samples of Sr2RuO4, a spin-triplet superconductor. With micrometer-sized annular-shaped samples, we observed transitions between integer fluxoid states as well as a regime characterized by "half-integer transitions"-steps in the magnetization with half the height of the ones we observed between integer fluxoid states. These half-height steps are consistent with the existence of half-quantum vortices in superconducting Sr2RuO4.