In this paper, we propose a new programmable Constant Phase Element (CPE) realization using resistive crossbar arrays. The programmability of the resistive devices is used to program the CPE. Due to the structure of the crossbar, a new approximation of the CPE element is investigated. The approximation consists of parallel branches where each one can be seen as a weighted sum of low and high pass filters having the same cut-off frequency (i.e., Lapicque model). The closed-form approximation expression is derived, and then the Flower Pollination Algorithm (FPA) is used to find the optimal values of the network components. Different design examples are given over the frequency range of 106-109 rad/s to prove the ability of this realization to achieve any fractional order with less than 5% relative error in both phase and pseudo-capacitance and to demonstrate its programmability. Monte-Carlo simulations are performed to evaluate the sensitivity of the proposed realization against device variability. In addition, the proposed realization is compared with two other state-of-art realizations showing comparable results as standalone realization and within fractional-order relaxation oscillator application.