Fingerspelling is a critical part of American Sign Language (ASL) recognition and has become an accessible optional text entry method for Deaf and Hard of Hearing (DHH) individuals. In this paper, we introduce SpellRing, a single smart ring worn on the thumb that recognizes words continuously fingerspelled in ASL. SpellRing uses active acoustic sensing (via a microphone and speaker) and an inertial measurement unit (IMU) to track handshape and movement, which are processed through a deep learning algorithm using Connectionist Temporal Classification (CTC) loss. We evaluated the system with 20 ASL signers (13 fluent and 7 learners), using the MacKenzie-Soukoref Phrase Set of 1,164 words and 100 phrases. Offline evaluation yielded top-1 and top-5 word recognition accuracies of 82.45% (9.67%) and 92.42% (5.70%), respectively. In real-time, the system achieved a word error rate (WER) of 0.099 (0.039) on the phrases. Based on these results, we discuss key lessons and design implications for future minimally obtrusive ASL recognition wearables.