The 236 U(n, γ) reaction cross section has been measured for the incident neutron energy range from 10 eV to 800 keV using the DANCE γ-ray calorimeter at the Los Alamos Neutron Science Center. The cross section was determined with the ratio method, a novel technique using the 235 U(n, f ) reaction as a reference. The results of the experiment are reported in the resolved and unresolved resonance energy regions. Individual neutron resonance parameters were obtained below 1 keV incident energy using the R-Matrix code sammy. The cross section in the unresolved resonance region is determined with improved experimental uncertainty. It agrees with both ENDF/B-VII.1 and JEFF-3.2 nuclear data libraries. The results above 10 keV agree better with the JEFF-3.2 library.