This paper presents the design, the fabrication and the characterization of Schottky graphene/silicon photodetectors, operating at both 2 micron and room temperature. The graphene/silicon junction has been carefully: characterized device shows a non ideal behaviour with the increasing temperature and the interfacial trap density has been measured as 1.1 x10^ 14 eV^-1cm^-2. Photodetectors are characterized by an internal (external) responsivity of 10.3 mA/W (0.16 mA/W) in an excellent agreement with the theory. Our devices pave the way for developing hybrid graphene-Si free-space illuminated PDs operating at 2 micron, for free-space optical communications, optical coherence tomography and light-radars.