X-ray diffraction measurements on alpha-solid oxygen under an applied magnetic field are reported. The volume of alpha-solid O2 is found to expand with increasing magnetic field: the lattice constants a and b elongate, while the lattice constant c and the angle beta are almost independent of the magnetic field. The maximum volume expansion observed is about 1% under a 7.5 T field, which is a giant effect compared to the volume change observed in ferromagnetic metals, such as Fe, Co and Ni. This finding indicates that a spin-dependent inter-molecular potential is essential in determining the structure of alpha-solid O2. The experimental results conform with predictions based on a magneto-elastic interaction derived from an antiferromagnetic exchange coupling of O2 spins.