Yes, but do it carefully.
Green Grass Clippings
Green grass clippings should be considered a nitrogen or worm food source. So, when adding green grass clippings to your worm bin, you should add them in the same proportions as you would other worm food. It is best to sprinkle or spread out the grass clippings in your worm bin so that they don’t stick together and form a ball of wet grass clippings that will be harder for your composting worms to eat.
Most worm composters do not use green grass clippings as a food source for their composting worms because they have enough food scraps coming out of their kitchens to keep their composting worms happily eating.
Brown Grass Clippings
If you spread your grass clippings out on concrete on a sunny day until they turn brown then they are more like a carbon source and should be treated like worm bin bedding. This will allow you to add much more grass clippings to your worm bin. However, it is super annoying to do.
Contamination from Yard Sprays
Many homeowners and landscapers spray their lawns with fertilizers and insecticides. This residue can stay on the grass clippings and may hurt your worms if you add the grass clippings to your worm bin. It is best to only use grass clippings from your own yard where you can control what has been sprayed to your grass.
Buy a mulching lawn mower that returns your chewed up bits of grass to your lawn as you mow. Mulching lawn mowers keep you from having to throw away a bag of grass clippings (or even deal with it at all) and it is super beneficial for your lawn.