Ever since gravitational waves were experimentally detected and measured by LIGO, there has been multiple attempts to connect the theory of gravity with quantum physics. While LIGO probes the metric directly via interference, we probe the coupling of propagating gravitational waves to the quantum spin degree of freedom of a single electron — inspired by quantum sensing devices emerging as tools for fundamental physics. The predicted energy splitting of a hydrogen 2p state is $\Delta E \approx 1.89 \times 10^-47$ eV for a dimensionless LIGO-event strain amplitude $h= 10^-21$ at 100 Hz, nineteen orders of magnitude below current sensitivity—establishing the fundamental detection challenge.