Garlic powder clumps up
It sounds like you've got at least two problems: 


First, without a lid, it absorbs moisture from the air.  
Second, shaking it over hot food delivers steam directly to the powder
Possibly third, the holes in the shaker may be small enough to block as soon as the smallest clumps form.


Rice will act as a desiccant and absorb water, but its capacity to do so is actually quite limited.  I have a few pre-mixed spice grinders (garlic, chilli flakes, salt etc.) and they specifically say they're not meant for grinding directly over hot food.

So what can you do about it?  Using a small shaker (so it doesn't hang around too long) with a lid for storage will help but, maybe not enough . If you really want the garlic powder sprinkled rather than spooned, then you could keep it in an airtight container and spoon some into a tea strainer when needed.