This article is from the Apple II Csa2 FAQ, by Jeff Hurlburt with numerous contributions by others.
No. The Apple III joystick port has very little in common with the Apple II one. The Apple III joystick's internal circuit arrangement and plug pinout are very different from that for an Apple II joystick. Do not attempt to connect an Apple II joystick to an Apple III, or vice versa. At the very least, it will not work. At worst, you could damage the computer. Here are the joystick port pinouts, for comparison:II III 1 SW1 GND 2 +5V +5V 3 GND GND 4 PDL2 Joy-X 5 PDL0 SW0 6 SW2 +12V 7 SW0 GND 8 PDL1 Joy-Y 9 PLD3 SW1By: David Empson