Charge transport in organic semiconductors is strongly dependent on the molecular orientation and packing, such that manipulation of this molecular packing is a proven technique for enhancing the charge mobility in organic transistors. However, quantitative measurements of molecular orientation in micrometre-scale structures are experimentally challenging. Several research groups have suggested polarised Raman spectroscopy as a suitable technique for these measurements and have been able to partially characterise molecular orientations using one or two orientation parameters. Here we demonstrate a new approach that allows quantitative measurements of molecular orientations in terms of three parameters, offering the complete characterisation of a three-dimensional orientation. We apply this new method to organic semiconductor molecules in a single crystal field-effect transistor in order to correlate the measured orientation with charge carrier mobility measurements. This approach offers the opportunity for micrometre resolution (diffraction limited) spatial mapping of molecular orientation using bench-top apparatus, enabling a rational approach towards controlling this orientation to achieve optimum device performance.