The sign for ringing as in "a ringing phone" (or an alarm) is done by whacking (that is a technical term folks) an index finger up against the palm of the non-dominant hand twice.
Notes:
If you mean "ringing" as in my ears are ringing you might indeed see some people sign: MY EAR RINGING using the above sign but if you are taking about a hearing aid squealing then instead use an "E" handshape near the ear and move it out away from the ear using a bit of a wobbly movement.
Notes: