You can attempt a weld of the acrylic. Get some acrylic glue, a needle and syringe (try a 30 gauge 1/2 needle). You can use small insulin syringe/needle set up as well.
Clean with alcohol thoroughly. Do NOT use acetone at all. Then watch a video on youtube on how to weld acrylic (very simple really). Think about how you'll hold/clamp/tape the piece on one the glue is in place. Allow no less than 72 hours to cure before thinking about using it again.
It may not be as strong as the original, but the forces on that piece aren't typically severe and I truly believe you'll have it hold.
I've fixed several pieces and built several boxes (acrylic) without much fuss. Most videos on internet last 2-4 minutes, and are pretty easy to understand. Materials cost will be very cheap.