Context.A variety of kinetic electrostatic and electromagnetic waves develop in the solar wind and the relationship between these waves and larger scale structures, such as current sheets and ongoing turbulence, remain a topic of investigation. Similarly, the instabilities producing ion-acoustic waves in the solar wind are still an open question.Aims.The goals of this paper are to investigate electrostatic Langmuir and ion-acoustic waves in the solar wind at 0.5 AU and determine whether current sheets and associated streaming instabilities can produce the observed waves. The relationship between these waves and currents observed in the solar wind is investigated statistically.Methods.Solar Orbiter’s Radio and Plasma Waves instrument suite provides high-resolution snapshots of the fluctuating electric field. The Low Frequency Receiver resolves the waveforms of ion-acoustic waves and the Time Domain Sampler resolves the waveforms of both ion-acoustic and Langmuir waves. Using these waveform data, we determine when these waves are observed in relation to current structures in the solar wind, estimated from the background magnetic field.Results.Langmuir and ion-acoustic waves are frequently observed in the solar wind. Ion-acoustic waves are observed about 1% of the time at 0.5 AU. The waves are more likely to be observed in regions of enhanced currents. However, the waves typically do not occur at current structures themselves. The observed currents in the solar wind are too small to drive instability by the relative drift between single ion and electron populations. When multi-component ion or electron distributions are present, the observed currents may be sufficient for instabilities to occur. Ion beams are the most plausible source of ion-acoustic waves in the solar wind. The spacecraft potential is confirmed to be a reliable probe of the background electron density when comparing the peak frequencies of Langmuir waves with the plasma frequency calculated from the spacecraft potential.