Dialogue State Tracking (DST), a key component of task-oriented conversation systems, represents user intentions by determining the values of pre-defined slots in an ongoing dialogue. Existing approaches use hand-crafted templates and additional slot information to fine-tune and prompt large pre-trained language models and elicit slot values from the dialogue context. Significant manual effort and domain knowledge is required to design effective prompts, limiting the generalizability of these approaches to new domains and tasks. In this work, we propose DiSTRICT, a generalizable in-context tuning approach for DST that retrieves highly relevant training examples for a given dialogue to fine-tune the model without any hand-crafted templates. Experiments with the MultiWOZ benchmark datasets show that DiSTRICT outperforms existing approaches in various zero-shot and few-shot settings using a much smaller model, thereby providing an important advantage for real-world deployments that often have limited resource availability.