  Red giant stars present mixed modes, which behave as pressure modes in the
convective envelope and as gravity modes in the radiative interior. This mixed
character allows to probe the physical conditions in their core. With the
advent of long-duration time series from space-borne missions such as CoRoT and
Kepler, it becomes possible to study the red giant core rotation. As more than
15 000 red giant light curves have been recorded, it is crucial to develop a
robust and efficient method to measure this rotation. Such measurements of
thousands of mean core rotation would open the way to a deeper understanding of
the physical mechanisms that are able to transport angular momentum from the
core to the envelope in red giants. In this work, we detail the principle of
the method we developed to obtain automatic measurements of the red giant mean
core rotation. This method is based on the stretching of the oscillation
spectra and on the use of the so-called Hough transform. We finally validate
this method for stars on the red giant branch, where overlapping rotational
splittings and mixed-mode spacings produce complicated frequency spectra.
