Can I use an induction cooker to restore silica gel's water absorbency?
If you heat silica gel, you will drive out the water from it. What actually happens depends on how you heat it, and how hot it gets.

If you have a thick layer, you may not be able to effectively dehydrate the crystals in a reasonable time. 

If you try to use a gas oven, you're on a loser because burning gas makes water and carbon dioxide - it takes ages trying to do the job with moist heat.

You might be able to do a thin layer in the bottom of a pan on an induction cooker, but remember that you cannot achieve temperature control very easily. The optimum range to regenerate the silica gel is 120 degC to 140 degC, and you really want a gradual temperature rise to do the job effectively - better to hold the stuff at 80 to 90 deg C for half an hour before you go to 120 deg C. 

If you try to dehydrate too quickly, the crystals will crack and break up, so you may end up with a fine powder, rather than crystals.