We studied charge transport in a field-effect transistor based on an anthracene crystal by single-molecule spectroscopy at cryogenic temperatures. When applying a control voltage to the gate, source and drain electrodes, we observe spectral drifts of the probe molecules' lines, which follow strongly non-exponential (stretched) kinetics, from seconds to tens of minutes. Applying a gate voltage alone, we find a dependence of the spectral shift as the logarithm of time. When an additional source-drain voltage is applied, the spectral shift follows a power law of time, similar to the elementary step of conduction in amorphous solids, postulated in the continuous-time random walk theory of Scher and Montroll.