A new measurement of the $\theta_{13}$ mixing angle has been obtained at the Daya Bay Reactor Neutrino Experiment via the detection of inverse beta decays tagged by neutron capture on hydrogen. The antineutrino events for hydrogen capture are distinct from those for gadolinium capture with largely different systematic uncertainties, allowing a determination independent of the gadolinium-capture result and an improvement on the precision of $\theta_{13}$ measurement. With a 217-day antineutrino data set obtained with six antineutrino detectors and from six 2.9 GW$_{th}$ reactors, the rate deficit observed at the far hall is interpreted as $\sin^22\theta_{13}=0.083\pm0.018$ in the three-flavor oscillation model. When combined with the gadolinium-capture result from Daya Bay, we obtain $\sin^22\theta_{13}=0.089\pm0.008$ as the final result for the six-antineutrino-detector configuration of the Daya Bay experiment.