Many mobile systems and wearable devices, such as Virtual Reality (VR) or Augmented Reality (AR) headsets, lack a keyboard or touchscreen to type an ID and password for signing into a virtual website. However, they are usually equipped with gesture capture interfaces to allow the user to interact with the system directly with hand gestures. Although gesture-based authentication has been well-studied, less attention is paid to the gesture-based user identification problem, which is essentially an input method of account ID and an efficient searching and indexing method of a database of gesture signals. In this paper, we propose FMHash (i.e., Finger Motion Hash), a user identification framework that can generate a compact binary hash code from a piece of in-air-handwriting of an ID string. This hash code enables indexing and fast search of a large account database using the in-air-handwriting by a hash table. To demonstrate the effectiveness of the framework, we implemented a prototype and achieved 99.5% precision and 92.6% recall with exact hash code match on a dataset of 200 accounts collected by us. The ability of hashing in-air-handwriting pattern to binary code can be used to achieve convenient sign-in and sign-up with in-air-handwriting gesture ID on future mobile and wearable systems connected to the Internet.