In this paper we investigate \(L^p\) -estimates for Hörmander classes of pseudo-differential operators on the torus \(\mathbb {T}^n\) . Our results are framed within the global symbolic calculus developed by Ruzhansky and Turunen on \(\mathbb {T}^n \times \mathbb {Z}^n\) , by using the discrete Fourier analysis on the torus. This approach extends the classical \((\rho , \delta )\) -Hörmander classes to the toroidal setting. The main contributions of this work generalize the method of Álvarez and Hounie for \(\mathbb {R}^n\) to the torus, while also extending Fefferman’s \(L^p\) -boundedness theorem to the toroidal context, even in cases where \(\delta \ge \rho \) . When \(\delta \le \rho \) , our results align with and recover existing estimates found in the literature.