An analysis is carried out to study the flow generated in a semi-infinite expanse of an incompressible second-grade fluid bounded by a porous oscillating disk. The flow is due to non-coaxial rotations of a disk and a fluid at infinity. The fluid is electrically conducting in the presence of a uniform transverse magnetic field. The solutions of the developed flow are obtained for the cases when the angular velocity is greater than, smaller than, or equal to the frequency of oscillation. The velocity field is found analytically by a Laplace transform technique. It is found that for uniform suction and blowing at the disk, shear oscillations are confined to the Ekman-Hartmann layer near the disk for all values of the frequencies.