Sure! I’d recommend starting with this patch here, and use its save and load functions. The default format is "session" (set in storage.js), so you’ll need to change the value of storage_defaultformat to "local", but that should work pretty seamlessly otherwise!
To give your players the ability to actually save and load themselves, you’ll probably want to attach those things to a UI element (like an HTML button, as seen in Inky’s web player — the one get when you export a project to web).