We studied the single-layered iridate Sr2IrO4 with a scanning tunneling microscope. The finite low temperature conductance enables the electronic structure of this antiferromagnetic Mott insulator to be measured by tunneling spectroscopy. We imaged the topography of freshly cleaved surfaces and measured differential tunneling conductance at cryogenic temperatures. We found the Mott gap in the tunneling density of states to be 2 Delta = 615 meV. Within the Mott gap, additional shoulders are observed which are interpreted as inelastic loss features due to magnons.