Circular data can arise from many sources, such as image processing, protein structure, and geological data, just to name a few. Wrapped stable family of distributions constitute one of the most widely used class of distributions for the analysis of such data. Wrapped Cauchy distribution is a member of this family and it is the only one known to have a single term explicit pdf compared to the infinite series representations for all the others. We develop in this paper reference priors and probability matching priors for this distribution, which turn out to be quite elegant and provide good frequentist performance as well. (C) 2019 Elsevier B.V. All rights reserved.