I have a Parent Site List and Sub Site list, where I need to get data from multi-choice checkbox column box, convert it to a string and copy it to a list on a sub site.
Is there way to do this programmatically with SharePoint Online?
You can do with programming. In SharePoint Online, you can use Java Script Client Object Model. Check dis MSDN link to see a lot of examples:
How to: Complete basic operations using JavaScript library code in SharePoint 2013