It depends. There are two issues. One is heating of the wire and the other is the total voltage drop in the wire (down and back). The following page (at the bottom) includes a calculator that will give you the voltage drop in various length runs at different currents. http://www.powerstream.com/Wire_Size.htm
For a 10 foot length (that's 20 foot down and back) of copper wire you will get the following voltage drops at 20A:
#14 = 1.037V
#12 = 0.653V
#10 = 0.411V
If the radio draws 20A peak and works down to 11.5V and you want to operate from your battery until its down to about 12V then you need to use #10 wire if you have a 10-foot length of cable. That'll provide 11.589 V at the radio when the battery voltage is down to 12V.
If you were to use #14 then in order to maintain 11.5V at the radio the battery voltage would have to be maintained at or above 12.537V.