Accurate traffic forecasting at intersections governed by intelligent traffic signals is critical for the advancement of an effective intelligent traffic signal control system. However, due to the irregular traffic time series produced by intelligent intersections, the traffic forecasting task becomes much more intractable and imposes three major new challenges: 1) asynchronous spatial dependency, 2) irregular temporal dependency among traffic data, and 3) variable-length sequence to be predicted, which severely impede the performance of current traffic forecasting methods. To this end, we propose an Asynchronous Spatio-tEmporal graph convolutional nEtwoRk (ASeer) to predict the traffic states of the lanes entering intelligent intersections in a future time window. Specifically, by linking lanes via a traffic diffusion graph, we first propose an Asynchronous Graph Diffusion Network to model the asynchronous spatial dependency between the time-misaligned traffic state measurements of lanes. After that, to capture the temporal dependency within irregular traffic state sequence, a learnable personalized time encoding is devised to embed the continuous time for each lane. Then we propose a Transformable Time-aware Convolution Network that learns meta-filters to derive time-aware convolution filters with transformable filter sizes for efficient temporal convolution on the irregular sequence. Furthermore, a Semi-Autoregressive Prediction Network consisting of a state evolution unit and a semiautoregressive predictor is designed to effectively and efficiently predict variable-length traffic state sequences. Extensive experiments on two real-world datasets demonstrate the effectiveness of ASeer in six metrics.