Optical activity, the power of a medium to rotate the polarization of a light beam, has contributed significantly to molecular structure assessments in stereochemistry, biomolecular science and crystallography. Thus far, it is commonly believed that optical activity is manifested only in the chiral media which can give rise to circular birefringence of light. Here, we experimentally demonstrate that free space can also support the implementation of non-reciprocal optical activity with Bessel beams by spin-orbital interaction. Specifically, non-diffractive optically active beams are realized, with their optical rotatory power readily controlled by simple optical elements. We show that such free-space optical activity can be exploited to form non-reciprocal optical components such as polarization rotators, isolators, and circulators. Our results may bring about new possibilities of media-independent optical activity to other transverse waves ranging from radio to optical frequencies.