Graph or network representations are an important foundation for data mining and machine learning tasks in relational data. Many tools of network analysis, like centrality measures, information ranking, or cluster detection rest on the assumption that links capture direct influence, and that paths represent possible indirect influence. This assumption is invalidated in time-stamped network data capturing, e.g., dynamic social networks, biological sequences or financial transactions. In such data, for two time-stamped links (A,B) and (B,C) the chronological ordering and timing determines whether a causal path from node A via B to C exists. A number of works has shown that for that reason network analysis cannot be directly applied to time-stamped network data. Existing methods to address this issue require statistics on causal paths, which is computationally challenging for big data sets. Addressing this problem, we develop an efficient algorithm to count causal paths in time-stamped network data. Applying it to empirical data, we show that our method is more efficient than a baseline method implemented in an OpenSource data analytics package. Our method works efficiently for different values of the maximum time difference between consecutive links of a causal path and supports streaming scenarios. With it, we are closing a gap that hinders an efficient analysis of big time series data on complex networks.