In architectural construction, automated robotic assembly is challenging due to occurring tolerances, small series production and complex contact situations, especially in assembly of elements with form-closure such as timber structures with integral joints. This paper proposes to apply Reinforcement Learning to control robot movements in contact-rich and tolerance-prone assembly tasks and presents the first successful demonstration of this approach in the context of architectural construction. Exemplified by assembly of lap joints for custom timber frames, robot movements are guided by force/torque and pose data to insert a timber element in its mating counterpart(s). Using an adapted Ape-X DDPG algorithm, the control policy is trained entirely in simulation and successfully deployed in reality. The experiments show the policy can also generalize to situations in real world not seen in training, such as tolerances and shape variations. This caters to uncertainties occurring in construction processes and facilitates fabrication of differentiated, customized designs.