Yes. Sounds can be registered as trademarks in most jurisdictions, provided the sound is distinctive and functions as an identifier of a single commercial source.
The sound must not be functional (i.e., it cannot be a sound that is necessary to the use of the product) and must have the capacity to identify the origin of the goods or services rather than simply describe or accompany them. Well-known examples include the Intel chime and the MGM lion's roar.
In practice, sound marks are harder to register than wordmarks or logos. The applicant must represent the sound precisely in the application, typically as an audio file or musical notation, and demonstrate that consumers associate the sound with their brand specifically.