No, there is no branch of Engineering which relates to archaeology or history. Definitely there are branches like Applied Geology, Geophysical Technology, BS (Economics/Humanities), Mechanical Engineering, Mathematics which somewhat have excerpts and Historical Significances from Rock Ages, Research, History of Science and Technology, English and History of Manufacturing, however aim of Engineering is to provide future solutions, not date back events of past.

You may perhaps pursue Engineering, post which prepare for UPSC CSE and Government Engineering Exams, which greatly align with your Interests and Career Prospects.