I'm interested in knowing if there is an application (or is it possible) to read radio waves on a phone?

What do you mean by read ?
The iPhone already picks up many forms of radio waves, cell, wifi, bluetooth, audio broadcasts.

An App will do nothing if you don't have a means to tune, intercept and demodulate or differentiate and decode in some cases the signals on it.

Your phone is basically a mobile computer. A radio uses certain frequencies to intercept signals from the stations that operate at those frequencies. Your phone does not have the tuner that does that. But many radio stations have internet associated links to their over the air productions. So all you have to do is search the stations call sign on the net like WKRG or WKRG Minneapolis or whatever and you should be able to acquire the link and listen to music from your phone as long as that particular station is also on the net.

Not sure what you mean by "Read" Radio waves. They may have a Spectrum Analyzer App. Would Show Frequency. To do anything with the Interested Frequency, You would need more than a phone as there are so many methods to send Audio, Video, and Data.