  Measuring the stellar position angle provides valuable information on binary
stellar formation or stellar spin axis evolution. We aim to develop a method
for determining the absolute stellar position angle using spectro-astrometric
analysis of high resolution long-slit spectra. The method has been designed in
particular for slowly rotating stars. We investigate its applicability to
existing dispersive long-slit spectrographs, identified here by their plate
scale, and the size of the resulting stellar sample. The stellar rotation
induces a tilt in the stellar lines whose angle depends on the stellar position
angle and the orientation of the slit. We developed a rotation model to
calculate and reproduce the effects of stellar rotation on unreduced high
resolution stellar spectra. Then we retrieved the tilt amplitude using a
spectro-astrometric extraction of the position of the photocentre of the
spectrum. Finally we present two methods for analysing the position spectrum
using either direct measurement of the tilt or a cross-correlation analysis.
For stars with large apparent diameter and using a spectrograph with a small
plate scale, we show that it is possible to determine the stellar position
angle directly within 10deg with a signal-to-noise ratio of the order of 6.
Under less favourable conditions, i.e. larger plate scale or smaller stellar
diameter, the cross-correlation method yields comparable results. We show that
with the currently existing instruments, it is possible to determine the
stellar position angle of at least 50 stars precisely, mostly K-type giants
with apparent diameter down to 5 milliarcseconds. If we consider errors of
around 10deg still acceptable, we may include stars with apparent diameter down
to 2 mas in the sample that then comprises also some main sequence stars.
