An objective measurement of the debilitating symptom, chronic itch, is necessary for improvements in patient care for numerous medical conditions. While wearable devices have shown promise for scratch detection, they are currently unable to estimate scratch intensity, preventing a comprehensive understanding of the effect of itch on an individual. In this work, we present a framework for the estimation of scratch intensity in addition to scratch detection consisting of a multimodal wearable ring device and machine learning algorithms for regression of scratch intensity on a 0-600 mW mechanical power scale that can be mapped to a 0-10 continuous scale. We evaluate the performance of our algorithms on 20 individuals using Leave One Subject Out (LOSO) Cross Validation (CV) and using data from 14 additional participants, we show that our algorithms achieve clinically-relevant discrimination of scratching intensity levels. This work demonstrates that a finger-worn device can provide multidimensional, objective, real-time measures for the action of scratching.