While standard recurrent neural networks explicitly impose a chain structure on different forms of data, they do not have an explicit bias towards recursive self-instantiation where the extent of recursion is dynamic. Given diverse and even growing data modalities (e.g., logic, algorithmic input and output, music, code, images, and language) that can be expressed in sequences and may benefit from more architectural flexibility, we propose the self-instantiated recurrent unit (Self-IRU) with a novel inductive bias towards dynamic soft recursion. On one hand, theSelf-IRU is characterized by recursive self-instantiation via its gating functions, i.e., gating mechanisms of the Self-IRU are controlled by instances of the Self-IRU itself, which are repeatedly invoked in a recursive fashion. On the other hand, the extent of the Self-IRU recursion is controlled by gates whose values are between 0 and 1 and may vary across the temporal dimension of sequences, enabling dynamic soft recursion depth at each time step. The architectural flexibility and effectiveness of our proposed approach are demonstrated across multiple data modalities. For example, the Self-IRU achieves state-of-the-art performance on the logical inference dataset [Bowman et al., 2014] even when comparing with competitive models that have access to ground-truth syntactic information.