Epitaxial orthorhombic YMnO3 thin films, (0 0 1) oriented, have been grown by pulsed laser deposition on (0 0 1)SrTiO3 substrates. Their crystal structure and magnetic response have been studied in detail. Although bulk o-YMnO3 is antiferromagnetic, our magnetic measurements reveal intriguing thermal hysteresis between the zero-field-cooled and field-cooled curves below the onset of the antiferromagnetic ordering temperature, thus signaling a more complex magnetic structure with net ferromagnetic moments. We discuss on the possible origin of this net magnetization and we have found a correlation of the magnetic response with the strain state of the films. We propose that substrate-induced strain modifies the subtle competition of magnetic interactions and leads to a non-collinear magnetic state that can thus be tuned by strain engineering.