Well, ASA (acrylonitrile styrene acrylate) is very similar to ABS (acrylonitrile butadiene styrene), just with much better UV performance (especially with colors), so generally adhesives that are good with ABS are a good place to start for using with ASA. I’ve had a lot of success with SCIGRIP 16 plastic cement for acrylics.

For UV resistance, you can use a specialized adhesive like Araldite 2028-1 – it’s designed specifically for UV stability, for application with outdoor signage, and similar. It’s transparent though, which is a feature that appears to be irrelevant to your application.

Personally, I think that if you’re doing a one-off project, and want to be sure that it will have a long service life, just go with a two-part epoxy to bond it. I know it’s not as easy to use as an acrylic glue, but you only have to do it once. There are a few options from different brands, but I’ve used MG Chemicals 9200 epoxy adhesive before.

Just use super glue! Cyanoacrylates are a good bet with ASA, but you may want to get a specialized one rather than just from the dollar store. The UV exposure outdoors may be a risk.