When you make a custom field on the Project level, it should be searchable. I am assuming you are talking about the Project View > Filter Search box. Please see attached. All you need to do is click on the Icon next to search and click "Manage". There you could find the field you are looking for and you will then be able to filter it by that field. You can also search by the data within the field.
Also, if you are talking about the Project Property search box (the search box on each project), the field should be searchable by default.
However, to be on the same page, could you provide me a screenshot of which search box you are referring to?