The ability to count finger and wrist movements throughout the day with a nonobtrusive, wearable sensor could be useful for hand-related healthcare applications, including rehabilitation after a stroke, carpal tunnel syndrome, or hand surgery. Previous approaches have required the user to wear a ring with an embedded magnet or inertial measurement unit (IMU). Here, we demonstrate that it is possible to identify the occurrence of finger and wrist flexion/extension movements based on vibrations detected by a wrist-worn IMU. We developed an approach we call "Hand Activity Recognition through using a Convolutional neural network with Spectrograms" (HARCS) that trains a CNN based on the velocity/acceleration spectrograms that finger/wrist movements create. We validated HARCS with the wrist-worn IMU recordings obtained from twenty stroke survivors during their daily life, where the occurrence of finger/wrist movements was labeled using a previously validated algorithm called HAND using magnetic sensing. The daily number of finger/wrist movements identified by HARCS had a strong positive correlation to the daily number identified by HAND (R2 = 0.76, p < 0.001). HARCS was also 75% accurate when we labeled the finger/wrist movements performed by unimpaired participants using optical motion capture. Overall, the ringless sensing of finger/wrist movement occurrence is feasible, although real-world applications may require further accuracy improvements.