In online question-and-answer (QA) websites like Quora, one central issue is to find (invite) users who are able to provide answers to a given question and at the same time would be unlikely to say "no" to the invitation. The challenge is how to trade off the matching degree between users’ expertise and the question topic, and the likelihood of positive response from the invited users. In this paper, we formally formulate the problem and develop a weakly supervised factor graph (WeakFG) model to address the problem. The model explicitly captures expertise matching degree between questions and users. To model the likelihood that an invited user is willing to answer a specific question, we incorporate a set of correlations based on social identity theory into the WeakFG model. We use two different genres of datasets: QA-Expert and Paper-Reviewer, to validate the proposed model. Our experimental results show that the proposed model can significantly outperform (+1.5-10.7% by MAP) the state-of-the-art algorithms for matching users (experts) with community questions. We have also developed an online system to further demonstrate the advantages of the proposed method.