We propose ARISE, a framework that iteratively induces rules and generates synthetic data for text classification. We combine synthetic data generation and automatic rule induction, via bootstrapping, to iteratively filter the generated rules and data. We induce rules via inductive generalisation of syntactic n-grams, enabling us to capture a complementary source of supervision. These rules alone lead to performance gains in both, in-context learning (ICL) and fine-tuning (FT) settings. Similarly, use of augmented data from ARISE alone improves the performance for a model, outperforming configurations that rely on complex methods like contrastive learning. Further, our extensive experiments on various datasets covering three full-shot, eight few-shot and seven multilingual variant settings demonstrate that the rules and data we generate lead to performance improvements across these diverse domains and languages.