Incoherent digital holography is a promising solution for acquiring three-dimensional information in the form of interference without a laser. Self-interference is the principal phenomenon of incoherent holography which splits the incident light wave into two waves and interferes with each one. The characteristics of incoherent holograms are defined by the optical configuration of wavefront dividing units. In this paper, we propose the synthetic aperture method to achieve super-resolution of geometric phase lens-based self-interference incoherent digital holography. We analyze the resolution of incoherent holograms acquired from geometric phase lenses and experimentally demonstrate the resolution enhancement via the synthetic-aperture method. Moreover, the sparse synthetic-aperture method is proposed to ensure effective data capturing and the numerical optimization method is also proposed to fill the gap between the empty space of sparsely acquired holograms.