A popular science fiction technology is to use electromagnetic fields to manipulate the local geometry of space-time. All that general relativity says is that any form of energy can cause space-time to become curved. Too much curvature and you may end up with black holes or worm holes. The form of the energy can be anything; raw mass, the energy latent in electromagnetic fields, neutrinos etc. So, electromagnetic fields are not intimately related to space-time any more than mass is; its just another form of energy that can serve to generate curvature via its own gravitational field.
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All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the NASA Astronomy Cafe, part of the NASA Education and Public Outreach program.