Radio waves are part of the electromagnetic spectrum, which also includes visible light, infrared radiation, microwaves, gamma rays and other types of radiation.
Radio waves have the lowest frequencies in the electromagnetic spectrum, and therefore pose the least potential danger to humans.
Some types of electromagnetic radiation are harmful. These include microwaves, infrared radiation, x-rays and gamma rays. In general, the higher the frequency, the more harmful the type of electromagnetic radiation will be.
Electromagnetic radiation can be split into two types: Ionising and non-ionising. If radiation is ionising then it has enough energy to remove electrons from atoms and molecules.
Exposure to ionising radiation damages human tissue, which can lead to cell damage, cancer, radiation burns and radiation sickness.
Radio waves are non-ionising as they have the lowest frequencies of any waves in the electromagnetic spectrum and don’t carry enough energy to remove electrons from atoms or molecules.
It is the ability to remove electrons from atoms and molecules that makes other types of radiation harmful to humans.
Therefore, unlike higher-frequency electromagnetic radiation, radio waves are not thought to pose a risk of cancer by damaging the DNA in cells.
Potential radio wave dangers
Exposure to radio waves could cause nerve stimulation and tissue heating, but this would require a huge amount of exposure—much more than you’d receive just by listening to the radio.
You would only receive enough exposure for this to happen if you spent extended periods of time near a radio transmitter.
Mobile phones
Mobile phones use radio waves of a frequency that is higher frequency than waves used for FM broadcasts but not as high as waves used in microwave ovens.
Waves used mobile phone communication are thought to be safe, but the possibility that they may have some harmful effects on humans hasn’t been completely ruled out.
Additional sources:
https://www.cancer.org/cancer/cancer-causes/radiation-exposure/radiofrequency-radiation.html