Angular distributions for the 12C(d, p)13C transfer reactions have been measured at Ed = 11.8 MeV, and compared with those of the DWBA calculations. By means of this comparison, density distributions of the last neutron in the ground state and the first 1/2+ state of 13C are extracted. The properties of these states in 13C have also been studied in the framework of the nonlinear relativistic mean-field theory with NL-SH parameters. It is found that the first l/2+ state in 13C is a neutron halo state shown by both the experimental and theoretical density distributions of the last neutron. Angular distributions for the 12C (d, p) 13C transfer reactions have been measured at Ed = 11.8 MeV, and compared with those of the DWBA calculations. By means of this comparison, density distributions of the last neutron in the ground state and the first 1/2 + state of 13C are extracted. The properties of these states in 13C have also been studied in the framework of the nonlinear relativistic mean-field theory with NL-SH parameters. It is found that the first l / 2 + state in 13C is a neutron halo state shown by both experimental and theoretical density distributions of the last neutron.