This article investigates the torsion homology behaviour in towers of Oeljeklaus-Toma (OT) manifolds. This adapts an idea of Silver and Williams from knot theory to OT-manifolds and extends it to higher degree homology groups. In the case of surfaces, i.e. Inoue surfaces of type $S^{0}$, the torsion grows exponentially in both $H_{1}$ (as was established by Braunling) and $H_{2}$ (our result) according to a parameter which already plays a role in Inoue's classical paper, and we obtain that the torsion vanishes in all higher degrees. This motivates our presented machine calculations for OT-manifolds of higher dimension.