The stellar inclination angle - the angle between the rotation axis of a star and our line of sight - provides valuable information in many different areas, from the characterization of the geometry of exoplanetary and eclipsing binary systems to the formation and evolution of those systems. We propose a method based on asteroseismology and a Bayesian hierarchical scheme for extracting the inclination angle of a single star. This hierarchical method therefore provides a means to both accurately and robustly extract inclination angles from red giant stars. We successfully apply this technique to an artificial data set with an underlying isotropic inclination angle distribution to verify the method. We also apply this technique to 123 red giant stars observed with Kepler. We also show the need for a selection function to account for possible population-level biases, which are not present in individual star-by-star cases, in order to extend the hierarchical method towards inferring underlying population inclination angle distributions.