Fatigue-induced fractures constitute a major cause of failure in engineering components. Numerous conventional empirical and semi-empirical methodologies based on stress-life and strain-based approaches, have been developed for modeling fatigue in brittle materials. However, their application is not easily extendable to various materials, geometries, and loading histories. The phase field model for fracture is used for modeling fatigue [1] in diverse materials. Conventional phase field models consider the spectral or spherical decomposition of strain to account for the tension-compression asymmetry in isotropic materials. However, in the case of anisotropic linear elastic materials, the principal directions of stress and strain do not necessarily align, resulting in a lack of orthogonality. Moreover, the conventional phase field models consider the anisotropy in the crack propagation by merely modifying the fracture surface energy. To address the aforementioned limitation, Ziaei et al. [2] introduced a solution by proposing an orthogonal decomposition of constitutive relations into crack-driving and persistent components, specifically designed for materials exhibiting anisotropic properties. However, the work proposed by Ziaei et al. [2] was primarily focused on fracture in brittle materials and cannot be applied for fatigue failure. In this article, we have developed a phase field model for fatigue failure under anisotropic crack propagation by non-trivially extending the orthogonal decomposition proposed by [2] for the brittle fracture. We have utilized Gridap, an open-source finite element toolbox, in the Julia programming language for the numerical implementation of the proposed model following a similar procedure discussed in [3].