We present the operating principle and the first observing run of a novel kind of direct detector for axions and axion-like particles in the galactic halo. Sensitive to the polarisation rotation of linearly polarised laser light induced by an axion field, our experiment is the first detector of its kind collecting scientific data. We discuss our current peak sensitivity of \(1.51\times 10^{-10}\) \(\text{GeV}^{-1}\) (95 % confidence level) to the axion-photon coupling strength in the axion mass range of \(1.97\)-\(2.01\) \(\text{neV}\) which is, for instance, motivated by supersymmetric grand-unified theories. We also report on effects that arise in our high-finesse in-vacuum cavity at an unprecedented optical continuous-wave intensity of \(4.7\) \(\text{MW/cm}^2\). Our detector already belongs to the most sensitive direct searches within its measurement band, and our results pave the way towards surpassing the current sensitivity limits in the mass range from \(10^{-8}\) \(\text{eV}\) down to \(10^{-16}\) \(\text{eV}\) via quantum-enhanced laser interferometry.