The objective assessment of the prestige of an academic institution is a difficult and hotly debated task. In the last few years, different types of University Rankings have been proposed to quantify the excellence of different research institutions in the world. Albeit met with criticism in some cases, the relevance of university rankings is being increasingly acknowledged: indeed, rankings are having a major impact on the design of research policies, both at the institutional and governmental level. Yet, the debate on what rankings are {\em exactly} measuring is enduring. Here, we address the issue by measuring a quantitive and reliable proxy of the academic reputation of a given institution and by evaluating its correlation with different university rankings. Specifically, we study citation patterns among universities in five different Web of Science Subject Categories and use the \pr~algorithm on the five resulting citation networks. The rationale behind our work is that scientific citations are driven by the reputation of the reference so that the PageRank algorithm is expected to yield a rank which reflects the reputation of an academic institution in a specific field. Our results allow to quantifying the prestige of a set of institutions in a certain research field based only on hard bibliometric data. Given the volume of the data analysed, our findings are statistically robust and less prone to bias, at odds with ad--hoc surveys often employed by ranking bodies in order to attain similar results. Because our findings are found to correlate extremely well with the ARWU Subject rankings, the approach we propose in our paper may open the door to new, Academic Ranking methodologies that go beyond current methods by reconciling the qualitative evaluation of Academic Prestige with its quantitative measurements via publication impact.