As of UberMenu 2.3, you can turn on a custom javascript file in you UberMenu Control Panel just like with the custom CSS file. Activate it under Advanced Settings > Include Custom Javascript. This will automatically include the custom/custom.js file. Now rename custom-sample.js (found in the /custom folder) to custom.js and add your javascript to the file.
Heads up!
This archived doc is for an old version of UberMenu.
For the current documentation, please visit the UberMenu 3 Knowledgebase