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Yes, it is called acoustic communications. Here is an example of a paper that uses orthogonal frequency division multiplexing (OFDM) in an underwater acoustic channel.

EDIT:

Note that you wouldn't call it a SONAR any more because SONAR stands for SOund Navigation And Ranging, whereas this is a communication system, just like you wouldn't call your cell phone a radar.

EDIT 2:

Yes, the signal could be converted to a radio signal at a repeater. The repeater would ideally be floating in the surface and have a transducer (which is basically a microphone or array of microphones) on the underwater side to receive the sound waves. The transducer converts the sound waves into an electrical signal, which can be filtered and/or amplified, and then sent to an antenna for radio transmission. The antenna would likely need to be above water because radio waves don't propagate very far through water.

to be picky, RF is strongly attenuated is salt water.

Fresh water is much less attenuated. During WW2 submerged submarines could use their radios in Lake Michigan.

Very low frequency RF communications is possible in salt water. The bit rate is very low.

Fiber optic cables work well too.

Acoustics tend to be attenuated as well.

Yes, actually sound waves are better than RF signal in underwater, because of the low frequency requirement. We don't covert sound waves to radio signals. The transceiver in this case is called transducer.

EDIT: You have basically three options for wireless communication in underwater: RF signals, acoustic signals, and optical signals. RF signals suffer from large path loss, and the range of transmission is in meters. Optical signals suffer from scattering. Acoustic signals suffer from low propagation speed (~1500 m/s), but the transmission range is better than RF signals. Also, you don't need large antennas when transmitting low frequency acoustic signals, which is the case for RF signals. The bandwidth can be increased by using relay-assisted systems.

After a quick search, it seems that sonobuoys seem to have antennas that are kept above the surface to communicate with an aircraft or a ship. This is not an underwater wireless communication. The goal of underwater acoustic systems is to exchange information "wirelessly" between nodes underwater, and then with a central node at the surface that uses RF signals to communication with a center for further analysis/decisions.

You have 3 ways of communicating underwater

1) Acoustic : Most popular means of communication. Has high latency but good range

2) Low frequency RF. To increase the range you have to lower the frequency, which means small bandwidth, so you can't transmit a lot of information.

3) Optical: Low latency + High bandwidth but the range is limited to less than ~100 meters

This is incredibly common in aquatic robotics. There are multiple uses for underwater acoustic communication such as data transfer, localization to a surface vessel, mission control etc.

From a data transference point of view, yes; RF signals don't last well in salt water, whereas sound travels considerably better.

But...

If you're planning to try this on Earth, be aware that oceanic noise pollution is a problem, and if you need to communicate over large distances you'll need to make a loud noise. Consider using RF first; you'll get a low bit-rate, but it might be a better way to transfer the signal if the acoustic bands are already being used by marine life.

The best way for underwater communication is to be acoustic communication where sound waves are used. Sometimes, visible light is used such as red and green, but in all cases, acoustic communication is common and used more.

Underwater acoustic communication is considered as one of wireless networks types. but it's more complicated, I can say the most difficult environment to deal with.

The channel can't be time-invariant. however, in simulation, we can consider it as time-invariant, bit in reality it is not. It's considered as double selective channel. That makes the channel very difficult to estimate and equalize.

The bandwidth in underwater acoustic communication is very limited, that's another issue in that environment.

In most cases, there is not a LOS, it's very multi-path environment, and pathes are interfered with each other. Nowadays, OFDM is one of main solution for that, but because of the long delay, OFDM required longer CP, that will make the data rate limited too ! .. at the same time, the time variant channel required pilots for channel estimation which will make the data rate really limited too. (To generalize, the guard interval must be long to avoid the Inter symbol interference)

That area, is very common for searching and developing since it still has many many issues

Good luck