^ packer beat me to it. Polycarbonate is the other material you are probably thinking of.which is often confused with acrylic/perspex.
How about using a pressure sensitive acrylic adhesive sheet or even just double sided tape with an acrylic adhesive? (the former is just adhesive between to backing slips, the latter is a central substrate with adhesive both sides).
Double sided tape will have the best tolerance to a surface texture and be easier to apply. The film can be bought as huge sheets and results in a very thin bond (0.05mm) but can be fragile to handle. Both will be a lot less messy and using a liquid adhesive and a much more even bond thickness. I would suggest contacting Viking tapes with what materials you are bonding as they have a huge range including ones for difficult to bond plastics. It will also be fully removable if needed or permanent if you use a plastic primer that goes with the tapes.