The short answer is yes, but that wasn't always the case.
Using sound as a unique identifier for a brand hasn't been a marketing tool for very long. The first successful application for a sound mark was registered in 1978 and was filed by NBC, one of the country's largest media conglomerates. Thirty-five years out, it is still a notoriously long and difficult process. So when I'm asked by another business owner if they can trademark a sound, I always have to give a "yes, but..." answer for the following reasons.
Sound trademarks have extremely strict standards.
The Lanham Act, which established the main chunk of the U.S.'s modern trademark law, allows for "any word, name, symbol, or device" to be registered by that mark's owner as long as they have a bonafide right to its use and intend to use it in commerce. So there really isn't anything in the Lanham Act that precludes the registration of a sound mark. We have to turn to the decision that allowed NBC to register a mark for their chimes, catchily titled "In re General Electric Broadcasting Co.," to find the litmus test for determining if a sound can be registered. And it states that the sound has to be '...so inherently different or distinctive that it attaches to the subliminal mind of the listener, to be awakened when heard, and to be associated with the source or event...'
It's really, really hard to trademark a sound.
You need to be one of the biggest, strongest presences in your market before you can argue that the sound you use to distinguish your business has subliminally implanted itself in the mind of the listener. Harley-Davidson famously withdrew its application to register the sound of its V-Twin engines after six years of litigation. They just couldn't make the argument that the thumping of a revving Harley was distinct enough to warrant a mark. As I write this post, there are 558 records of marks that could not be represented with a drawing in the USPTO database. When you consider the fact that there are hundreds of thousands of registered trademarks, you begin to appreciate just how difficult it is to register a sound.
Most businesses are better off copyrighting sounds.
When you create a sound to use in your marketing, it is technically copyrighted once a tangible version is made. And, while you can definitely try and register a mark for it, it's usually a better idea to just register a copyright, instead of running the labyrinth of the USPTO.
Unlike a trademark which stays active as long as it's renewed and used, a copyright expires 60 years after its creator's death. But if your business is growing with such speed and ferocity that the 60-year post-death limitation might be an issue, a sound mark can probably be filed for it before it lapses into public domain. In the meantime, a registered copyright will allow you to enforce your ownership of the sound if someone else attempts to use it.
While I can appreciate the desire of a creator to fully protect their rights to their intellectual property, in most cases registering a sound mark with the USPTO is a lost cause. Unless you can hum your jingle to someone and they'll immediately tell you where it's from, you probably can't argue that you've pierced into their subliminal mind. Sound marks are an interesting development in marketing, and there is definitely a strong case for protecting the right of a mark's owner to register a sound, but most businesses shouldn't worry about trademarking a sound, as a copyright will do just fine.