Do you get actual 'static' (that crispy buzzy crackly sound AM radios make when between stations), or do you get hum? If you get static and no stations, then the radio needs other repairs, as Warren suggested. If you are getting hum (which some people mistake for static), then you need to replace the electrolytic filter capacitors, as they have likely dried up. I have not consulted the schematic to see if electrolytic filter capacitors are used, but most radios built after 1930 use these.
T.