In this paper, we propose a \textit{weak supervision} framework for neural ranking tasks based on the data programming paradigm \citep{Ratner2016}, which enables us to leverage multiple weak supervision signals from different sources. Empirically, we consider two sources of weak supervision signals, unsupervised ranking functions and semantic feature similarities. We train a BERT-based passage-ranking model (which achieves new state-of-the-art performances on two benchmark datasets with full supervision) in our weak supervision framework. Without using ground-truth training labels, BERT-PR models outperform BM25 baseline by a large margin on all three datasets and even beat the previous state-of-the-art results with full supervision on two of the datasets.