We report the discovery of variable circularly polarised radio emission associated with relativistic ejections from GRS 1915+105, based on observations with the Australia Telescope Compact Array (ATCA) and the Multi-Element Radio-Linked Interferometer Network (MERLIN). Following a radio flare in 2001 January, significant and variable circular polarisation, at a fractional level of 0.2-0.4%, was measured with ATCA at four frequencies between 1-9 GHz. Following an additional outburst 65 days later in 2001 March, further ATCA observations measured a comparable sign and level of circular polarisation at two frequencies. At this second epoch, contemporaneous MERLIN observations directly imaged a relativistic ejection event and allowed us to confidently associate both the circularly and linearly polarised emission with the relativistic ejecta, allowing a detailed measurement of the full polarisation properties in the optically thin phase. The fractional circular polarisation spectrum appears to flatten at higher frequencies in 2001 January, when there is strong evidence for multiple components at different optical depths. While we cannot conclusively distinguish between synchrotron or propagation-induced conversion as the origin of the circularly polarised component, we do not consider that coherent or birefringent scintillation mechanisms are likely. The implication is therefore that the ejections from GRS 1915+105 are associated with a significant population of low-energy electrons, with associated consequences for the energetics of relativistic ejection events. [abridged]