Can I use plastic edging to form a rectangular flower bed?

Yes you can. You can make ground stakes to put into each corner out of any scrap wood you have handy. You can paint the wood first to match the edging if you'd like. Pound your wooden stakes (maybe you chose 2x2s) into the ground and then cut your edging sides one at a time stopping after every cut to glue that end to your wood corner blocks. Ask at your home improvement store for help selecting an appropriate plastic-to-wood glue suitable for the type of plastic edging. (PVC notably requires specific adhesive) Measure twice and cut once with your edging to ensure sharp looking corners as they come together at the corner block.