Following ideas proposed by Seidel, we define a version of equivariant wrapped Floer homology using symplectic involutions. The main advantage of Seidel construct is that the definition of Floer differentials uses parametrized moduli space of continuation equations, for which no new analysis is needed. Furthermore, by simplifying the complex we obtain a Leray-Serre type spectral sequence. Using these techniques combined with Maslov type index theory, we explain how to get information of the minimal number of symmetric Reeb orbits.