By default the control isn't available in your custom classes.
You could update the existing control (but can be overwritten easily when upgrading or importing data).
- Go to the form controls module
- search for the custom table selector (or table item if you want just 1 row)
scroll to the scope
- select system tables (which includes your custom classes)
If this suits your needs you might be thinking about just cloning your own copy the form control so you're safe for upgrades and imports overwriting the default Kentico control.