Thesis editors typically edit student theses on the undergraduate degree, master's degree, or doctoral level. The work might entail simple checking for misspellings or grammar errors or it could include more complex edits for preciseness, coherence, flow, and citation format. If you hope to become a thesis editor, generally you will need at least a college degree.
To become a thesis editor, an undergraduate English major is not necessarily required; however, getting a bachelor's degree with a major in English can significantly help your career. Editing requires the kinds of skills you are most likely to learn if you major in English. Granted, if you do not major in English, a related major such as communications could be a useful major if you take coursework relevant to editing as part of your degree.
During the college years, doing an internship could be beneficial if being a thesis editor is your goal. The internship could be done in an academic setting or could be done in a journalism or other setting. Whichever setting you choose, the thing of most importance is that you get editing and writing experience. Editing and re-writing are both a part of what you will do once you become a thesis editor.
Also, getting a graduate degree such as a Master of Science (MS) or a Doctor of Philosophy (PhD) in English could be useful if you hope to become a thesis editor. Pursuing a graduate degree would enable you to learn more about editing and writing. In addition, having graduate-level education would distinguish you from the competition and could persuade prospective clients to pay you higher editing rates.
Of note, if you aspire to become a thesis editor, you could find a job in one of two ways. You could register with a company that employs editors on an independent contractor basis. Then, students who come to the company seeking editing services will end up having you edit their theses. Or, by contrast, you could become self-employed and find your own editing clients online or through joining a professional editing organization.
Keep in mind that it could take some time for you to gain a foothold in the editing field. If you work with a company, it could take time for your editing work to get noticed. Or, if you are self-employed, it could take some time for you to figure out a way to successfully market your editing services to students. Granted, once your editing work becomes known or once you successfully market your editing services to students, you will become a successful thesis editor.