This paper presents ResISC, an RNS-based integrated sensing and computing architecture enabling efficient edge AI. ResISC platform features (i) an in-sensor residue encoder converting images directly to RNS in the analog domain, (ii) an energy-efficient RNS-based processing-near-sensor CNN accelerator utilizing SOT-MRAM, and (iii) an innovative mixed-radix unit for efficient activation operations. By employing selective channel deactivation, ResISC reduces computation overhead by up to $89 \%$, while achieving a $3.4 \times$ improvement in power efficiency and up to a $71 \times$ reduction in execution time compared to processing-in-MRAM platforms. Experiments on various datasets demonstrate that ResISC achieves competitive accuracy levels (up to $94.63 \%$ on CIFAR-10) with minimal degradation, making it an ideal solution for power-constrained, real-time edge applications.