Accelerated photoacoustic tomography (PAT) reconstruction is important for real-time photoacoustic imaging (PAI) applications. PAT requires a reconstruction algorithm to reconstruct the detected photoacoustic signal in order to obtain the detected image of the tissue, which is usually an inverse problem. Different from the typical method for solving the inverse problems that defines a model and chooses an inference procedure, we propose to use the Recurrent Inference Machines (RIM) as a framework for PAT reconstruction. Our model performs an accelerated iterative reconstruction, and directly learns to solve the inverse problem in PAT using the information from a forward model that is based on k-space methods. As shown in experiments, our method achieves faster high-resolution PAT reconstruction, and outperforms another method based on deep neural network in some respects.