Many plastics can be joined with adhesives (glue). The glue must be suitable for the type of plastic. Called solvent adhesives, they work by melting the plastic and welding the surfaces together. Acrylic (Plexiglass) plastic -
Note - Many solvent glues and resins used in plastic production are toxic. Be careful to avoid both eye and skin contact. Some will absorb through human skin. Be sure to read the manufacturers recommendations and wear gloves when required.