Turn off the water supply to the toilet. Remove the toilet tank lid and set it aside in a safe location. Locate the filler valve assembly, which is usually found on the left side of the toilet tank. Lift up on the float lever and gently turn the top portion of the valve assembly counterclockwise until it lifts off the valve body. Move the valve top slightly to one side and rest it on the edge of the toilet tank.
Hold a small, cup-shaped container over the open hole in the valve body to deflect water back into the tank. Turn on the water supply to flush the valve body and supply line. Turn off the water.
Clean any debris away from the valve seat at the bottom of the valve body hole using a paper towel. Turn the top of the filler valve upside down and examine the rubber seal. Clean any debris or deposits from the seal with a paper towel.
Reinstall the top of the valve by placing it on the valve body and turning it clockwise while lifting up on the float arm. Put the cover back on the tank. Turn on the water. Flush the toilet to see if the valve still whistles. If the noise persists, replace the filler valve.