The answer is YES you can.
Here are some cool how-to(s) to make your own Web Shooter ?
This video guide is made by Miles Morales himself (Haha) . No, it's made by odd producksins. It's not as hard as it looks but the guy has explained the procedure.
This video is by Jlazervideo.
Web Shooter 2.0, this is another one by Jlazervideo.
This video is made by LazerGadgets. This is definitely the most creative idea among all other video guides here and my personal favourite.
This the easiest, made with most paper and cardboard and thread obviously, also the one you can make quicker than all others. Made by CrazyPT.
So, have great time making and using your own Spider-Man Web Shooters.
Follow the collection for more good stuff coming soon.