We measured the total reaction cross sections of 12N in Si at 36.2 MeV/u using Radioactive Ion Beam Line in Lanzhou (RIBLL) with a new method. The reaction target was installed at the intermediate focusing point T1 at RIBLL. This scheme allows us to identify particles before and after the reaction target unambiguously. The total reaction cross section (1760±78 mb) of ^12N in Si is obtained. Assuming that ^12N consists of a core ^11C plus one halo proton, the excitation function of 12N on the Si and C targets is calculated with the Glauber model and the Fermi-Fermi density distributions. It can fit the experimental data very well. A large diffusion of the protons density distribution supports the halo structure for ^12N.