I just install my hot tub into my deck 1 month ago. I have noticed that the tub level has gone from 1/4" difference to about 3/4". Is this just settling?

Can I re-level the tub with shims or something??

My slab is about 6" below the ground level. I have had a drain installed to help remove water...

What can I do?

If you can afford to raise the tub about 2", I would take and etch the concrete slab with that stuff you use to make old concrete capabable of accepting new concrete (I forget the name off the top of my head) and add 2" of fresh concrete on top to form a new level surface. What happened most likely is your existing slab wasn't prepared properly and has settled under the weight of all that water.

DON'T SHIM

as this could cause cracking and breaking of your tub shell.