This paper deals with distributed state estimation (DSE) over a peer-to-peer (P2P) multi-agent system (MAS) with time-misaligned agents. A Bayes filter, which recursively computes the state posterior, is run at each agent and the Generalized Covariance Intersection (GCI) fusion is employed to aggregate the local posteriors of agents. However, due to the lack of a common time reference, time alignment (TA) among agents needs to be carried out jointly with state estimation. To this end, a cost function of the TA parameters is constructed by exploiting an information-theoretic interpretation of GCI fusion, so that TA can be accomplished by minimizing such cost. Further, an on-line optimization strategy is designed so as to recast the cost function into a quadratic form which can be easily minimized in real-time. The performance of the proposed distributed joint state estimation and TA algorithm is assessed by simulation experiments.