The effective mass, sheet carrier concentration, and mobility of electrons within a two-dimensional electron gas in an AlGaN/GaN heterostructure were determined using a laboratory-based terahertz cyclotron resonance spectrometer. The ability to perform terahertz cyclotron resonance spectroscopy with magnetic fields of up to 31 T was enabled by combining a high-field pulsed magnet with a modified asynchronous optical sampling terahertz detection scheme. This scheme allowed around 100 transmitted terahertz waveforms to be recorded over the 14 ms magnetic field pulse duration. The sheet density and mobility were measured to be 8.0 × 1012 cm−2 and 9000 cm2 V−1 s−1 at 77 K. The in-plane electron effective mass at the band edge was determined to be 0.228 ± 0.002m0.