How do I have a URI send Tasker an intent?
The creator of Tasker gave me some guidance here. Apparently Tasker's plugin AutoTools has the built-in scheme autotoolscommand:// built in, which will redirect everything following to an AutoApps command. Using the guide on AutoApps commands, I was able to easily figure out how to do this.

To set it up, create a profile for the AutoApps command of your choosing, e.g. myapp=:=. Then put the url of your link as autotoolscommand://myapp=:=?param=abc123. This will then set the Tasker variable %aacomm to ?param=abc123, which you can then parse or do whatever you wanted with. For me, I wanted to run a Variable Search Replace then to get just the data parts of the query with the regex (?&lt;==)[^&amp;]+.