The differential cross section for elastic scattering of protons from C13 has been measured to an accuracy of 7% for proton energies from 1.0 to 2.6 MeV at center-of-mass scattering angles of 39.2°, 54.7°. 90.0°, and 125.3°. Thin targets were prepared from methyl iodide enriched to 62% in C13 and the scattered protons were analyzed using a double-focusing magnetic spectrometer. Proton groups corresponding to C12 and C13 were cleanly separated except for energies below 1.8 MeV at 39.2° and 54.7°. A theoretical curve calculated from a two-level formula was fitted to the data over the entire energy range. Seven resonances, all previously observed, were necessary to fit the data. The laboratory resonance energies (MeV), center-of-mass reduced widths (MeV cm×10-13) and Jπ values assigned in this analysis are as follows: 1.150+/-0.002, 0.19, 0+; 1.366+/-0.050, 3.60, 0-; 1.461+/-0.003, 1.76, 3-, 1.540+/-0.003, 0.09, 2+; 1.980+/-0.003, 0.45, 3-(2-); 2.110+/-0.003, 1.66, 2-; 2.319+/-0.005, 0.09, 1+. These resonance energies and reduced widths are in fair agreement with previous measurements. The spin and parity assignments for all levels, except those at Ep=1.540 MeV and 1.980 MeV, confirm previous experiments. The 1.540-MeV resonance had previously been assumed to have Jπ=1+ and the 1.980-MeV resonance had been assigned Jπ=1-. Comparison of experiment and theory suggests the possibility of a broad resonance having J<=1 in the vicinity of Ep=2.8 MeV.