My kayak’s rudder has the squeak’s. When I use my foot pedal to change the direction of the rudder I can hear the the rudder squeak.
Is there a simple solution to this?
Simple solution? Yes! …
Remove the offending contraption! 
Being a longtime devotee of the “Dark Side Church of No Rudder/No Skeg”, my experience with rudders is, admittedly, limited (I have paddled many boats with rudders attached, though not for several years now). Lack of knowledge and experience, however, has never managed to still my fingers on this keyboard when I have nothing to say, yet feel the need to express it anyway.
The first and most obvious bit of nothingness I can offer is to recommend that you find the point of friction, thereby discovering the problem. Perhaps have someone wander around the boat as you work the pedals and recreate the squeak. Once the problem has been positively identified, you should be able to figure out a solution (is something bent and rubbing where it shouldn’t? is there friction along the cables? etc.).
This has been my longwinded way of suggesting that identification and diagnosis is your first step towards a solution (you may even figure out the solution the very moment you identify the source). So, have you identified the source of the squeak?
Melissa