We present Circuit-GNN, a graph neural network (GNN) model for designing distributed circuits. Today, designing distributed circuits is a slow process that can take months from an expert engineer. Our model both automates and speeds up the process. The model learns to simulate the electromagnetic (EM) properties of distributed circuits. Hence, it can be used to replace traditional EM simulators, which typically take tens of minutes for each design iteration. Further, by leveraging neural networks' differentiability, we can use our model to solve the inverse problem -- i.e., given desirable EM specifications, we propagate the gradient to optimize the circuit parameters and topology to satisfy the specifications. We exploit the flexibility of GNN to create one model that works for different circuit topologies. We compare our model with a commercial simulator showing that it reduces simulation time by four orders of magnitude. We also demonstrate the value of our model by using it to design a Terahertz channelizer, a difficult task that requires a specialized expert. The results show that our model produces a channelizer whose performance is as good as a manually optimized design, and can save the expert several weeks of topology and parameter optimization. Most interestingly, our model comes up with new designs that differ from the limited templates commonly used by engineers in the field, hence significantly expanding the design space.