After a lot of trial and error I found a way how to do this for iOS
Export your game as iOS project and open it in XCode
In the Info tab in XCode, add a URL type. For Indentifier use your app identifier in reverse domain name format, for example com.mydomain.myapp. For URL scheme use your app name, for example myapp.
Now comes the tricky part. I'm open to better suggestions because my solution involves adding some code manually, and I realise this is not ideal.
In CDVAppDelegate.m, in the function didFinishLaunchingWithOptions add this code (after the comment lines that are already there):
This code defines a NSURL object (named url) that holds the URL that was used to start the app. If url is not empty, the URL parameterstring (url.query) is added to the startpage string as parameterstring.
After building and installing on your device, you can now launch your app on your device using a URL with parameters, for example myapp://main?test=test123