During the past 10 years the unprecedented quality and frequency resolution of asteroseismic data provided by space photometry has revolutionized the study of red-giant stars providing us with the possibility to probe the interior of thousands of these targets. Our aim is to present an asteroseismic tool which allows to determine the total angular momentum of stars, without a priori inference of their internal rotational profile. We adopt and adapt to red giants the asteroseismic inversion technique developed for the case of the Sun. The method has been tested assuming different artificial sets of data, including also modes with harmonic degree l> 1. We estimate with an accuracy of 14.5% the total angular momentum of the red-giant star KIC 4448777 observed by Kepler during the first four consecutive years of operation.} Our results indicate that the measurement of the total angular momentum of red-giant stars can be determined with a fairly high precision by means of asteroseismology by using a small set of rotational splittings of only dipolar modes and that our method, based on observations of stellar pulsations, provides a powerful mean for testing and modeling transport of angular momentum in stars.
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