Many applications in information retrieval, natural language processing, data mining, and related fields require a ranking of instances with respect to a specified criteria as opposed to a classification. Furthermore, for many such problems, multiple established ranking models have been well studied and it is desirable to combine their results into a joint ranking, a formalism denoted as rank aggregation. This work presents a novel unsupervised learning algorithm for rank aggregation (ULARA) which returns a linear combination of the individual ranking functions based on the principle of rewarding ordering agreement between the rankers. In addition to presenting ULARA, we demonstrate its effectiveness on a data fusion task across ad hoc retrieval systems.