In this paper, we propose an ACT-R cognitive model for making credibility judgments about the credibility of Twitter authors. We abstracted the cognitive processes involved in three levels: attending to information on Web page, comprehending information to identify credibility cues, and integrating credibility cues to make a judgment. We represent basic knowledge required for making credibility judgment using declarative memory in ACT-R which is seeded with experiences of Twitter messages that have been passed through a Latent Dirichlet Allocation topic modeling process. Comparisons of model credibility judgments to human credibility judgments from controlled experiments show weak to strong correlations that range from r = 0.31 to r = 0.83 depending on the specific task.