Getting rid of RF interference can be rally difficult at times. Chokes or filters on the refrigerator's power leads may help but if it's being broadcast by the circuits in the refrigerator, it will be nearly impossible to get rid of.
Someone asked if this was when running on shore power, battery power, or both and the answer to this question is a very important piece of the troubleshooting process. If it's only on shore power, the 120 volt leads are the place to start. Be very careful working around 120 volt power and be sure any filters you install are designed for 120 volts. You may get the best answer from the manufacturer of the refrigerator. Yours is probably not the first to cause interference on AM radio.
With the refrigerator running and interference on the radio, unplug the radio antenna at the back of the radio. Is the noise still there or did it stop ?(of course the station will no longer be heard). If the noise stopped, the interference is being transmitted through the air just like a miniature radio station. The simplest solution to your problem may be to move the antenna farther from the refrigerator. Use a portable AM radio to see how far from the refrigerator you have to get for the noise to go away. Other things to try would be filters on the refrigerator power leads, making sure any parts of the refrigerator that are supposed to be grounded are actually grounded (with clean solid connections), and constructing a shield for the refrigerator's circuits.
If the noise continues, it's coming through the power wires and filters on these wires would be the thing to try.
At some point, you may have to give up and turn this over to a pro with the equipment and experience to correct your problem.