In this article a micro-cavity integrated graphene photodetector is proposed and numerically investigated for free space communications at mid-IR and long-IR wavelength domains. The structure is composed of single graphene layer(s) sandwiched between two distributed Bragg reflectors (DBRs). Light absorption in graphene is enhanced due to the cavity resonance reaching values as high as 80% of the incoming light power. Generated photo-carriers move toward the electrical contacts under an applied drain-source voltage. Responsivity of the photodetector at a wavelength of $\lambda=4.51\mu\mathrm{m}$ reaches values of 15 mA/W and 300 mA/W for $\mathbf{V}_{\mathbf{DS}}=0.2$ V and $\mathbf{V}_{\mathbf{DS}}=4$ V respectively.