How to add Option Group to Event Online Registration?
Shaun, Welcome to CiviCRM SE,

You will need to 


Add a custom group extending participant (CiviCRM >> Administer >> Customize Data and Screens >> Custom fields)
Add custom field of type select/radio/checkbox in a custom group created in #1.
Include this custom field in your profile which you are thinking to include for event.


Note: Custom field UI doesn't provide option to select existing option group which is not part of any custom field, you can either re-enter the options again or save the form without options and using api/sql update the option_group_id(with the option group id you have already created) column in civicrm_custom_field table for custom field you created at #2.

Thanks

Pradeep