The composition of the scientific workforce shapes the direction of scientific research, directly through the selection of questions to investigate, and indirectly through its influence on the training of future scientists. In most fields, however, complete census information is difficult to obtain, complicating efforts to study workforce dynamics and the effects of policy. This is particularly true in computer science, which lacks a single, all-encompassing directory or professional organization. A full census of computer science would serve many purposes, not the least of which is a better understanding of the trends and causes of unequal representation in computing. Previous academic census efforts have relied on narrow or biased samples, or on professional society membership rolls. A full census can be constructed directly from online departmental faculty directories, but doing so by hand is prohibitively expensive and time-consuming. Here, we introduce a topical web crawler for automating the collection of faculty information from web-based department rosters, and demonstrate the resulting system on the 205 PhD-granting computer science departments in the U.S. and Canada. This method constructs a complete census of the field within a few minutes, and achieves over 99% precision and recall. We conclude by comparing the resulting 2017 census to a hand-curated 2011 census to quantify turnover and retention in computer science, in general and for female faculty in particular, demonstrating the types of analysis made possible by automated census construction.