You actually have several options!
CA glue clouds the acrylic because of the solvents.
2-component Epoxy and Urethane adhesives are good options because they are solvent free and won’t attack the acrylic.
You will have to scuff the acrylic to promote adhesion. You can lay down two strips of masking tape on either side of the glue joint though to help keep both the scuffing and gluing neat and tidy if the aesthetics are important.
Depending how much strength you need, I like to also glue angles (like steel or aluminum angles) into the corners on either side of the face/edge joint. This increases the surface area of the joint and boosts strength many many times over that of the joint alone. This wouldnt be needed if all edges of the part are glued together thus locking it rigid, but say you’re just making a Tee-shaped item, the leverage the long part gives you can eventually cause a joint failure.
Here’s one that’s readily available at any wal mart, home improvement or hardware store.