We present a measurement of the energy spectrum of the light mass group of cosmic rays (protons and helium) with the High Altitude Water Cherenkov (HAWC) Observatory in the energy interval from \(10\) TeV to \(200\) TeV. The spectrum covers the energy range between direct and indirect measurements, where precision data on the composition of cosmic rays are needed. The spectrum was constructed by applying an unfolding technique on a proton plus helium enriched sub-sample (\(>90\%\) abundance) of cosmic ray air showers selected from the HAWC cosmic-ray data. The subset contains \(3.8 \times 10^{9}\) air shower events with primary energies in the interval \(1\) TeV to \(300\) TeV and zenith angles less than \(16.7\) degrees. Mass selection was performed using an analysis of the lateral age parameter of air shower events, based on both CORSIKA/QGSJET-II-03 simulations and event-by-event measurements on the lateral structure of the shower front and the primary energy of the showers.