  Using time-domain terahertz spectroscopy in pulsed magnetic fields up to 31
T, we measure the terahertz optical conductivity in an optimally-doped thin
film of the high temperature superconducting cuprate
La$_{1.84}$Sr$_{0.16}$CuO$_4$. We observe systematic changes in the
circularly-polarized complex optical conductivity that are consistent with
cyclotron absorption of p-type charge carriers characterized by a cyclotron
mass of $4.9\pm 0.8$ $m_{\rm e}$, and a scattering rate that increases with
magnetic field. These results open the door to studies aimed at characterizing
the degree to which electron-electron interactions influence carrier masses in
cuprate superconductors.
