Is it the bolt holding the yoke of the PTO to the shaft of tiller? (From you're picture it appears to be a phillips head screw.)
Is the yoke loose on the shaft?
If you're determined to remove the broken bolt, I would suggest getting a nut larger then the bolt dia., set it on top where the head of the bolt should be and weld it to the broken bolt.
The heat from the weld will help to break rust loose, but before you try to turn the welded nut give a good bath of KROIL or similar solvent. A 50/50 solution of acetone and auto. transmission fluid works excellent, also BUT acetone is flammable!!
Turn the nut clockwise a deg. and counter-clockwise a deg. to try to get any movement. Don't just try to power it out right away counterclockwise.
A wire welder is easier to get to the top of the broken bolt, but with a steady hand a stick welder will work fine. Get good perpetration at the bottom and come up making it one glob of metal (with a hex shape on the outside).
Have fun.....or just use it as it is for a while!