We give a complete classification of torsion pairs in repetitive cluster categories of type $A_n$, which were defined by Zhu as the orbit categories, via certain configurations of diagonals, called Ptolemy diagrams. As applications, we classify rigid subcategories, which gives Lamberti's classification of cluster tilting subcategories. When $p = 1$, this generalizes the work of Holm, Jorgensen and Rubey for the classification of torsion pairs in cluster categories of type $A_n$.