Adding a theme option to the admin that lets me turn on/off a javascript file

Yep you can use add_settings() to create the setting itself. There is an example in the codex.

This example code could go in your themes functions.php file or in a plugin file, it’s up to you.

Then in the header template all you would have to do is use an if statement to check what the value of the aforementioned setting was and either output the JS link or not based upon this variable.