Answer:
No. YOU cannot have anyone deported.
Only Immigration and Customs Enforcement can do so. Presently ICE is only focusing on crime-related deportations (since many "illegal" immigrants entered the country legally and were properly inspected but either had visas expire due to a variety of reasons some of which even include errors and oversights at DHS and USCIS (and its predecessor, INS) and is not pursuing otherwise law-abiding (and in most cases tax-paying) immigrants who have fallen out of status.
You can, of course, report the individual to ICE but, if they do take action against them improperly you could very well be civilly liable to the person yourself if it is determined that your report to ICE was improper and selfishly or racially motivated.