  We formulate a numerical method for predicting the tensorial linear response
of a rigid, asymmetrically charged body to an applied electric field. This
prediction requires calculating the response of the fluid to the Stokes drag
forces on the moving body and on the countercharges near its surface. To
determine the fluid's motion, we represent both the body and the countercharges
using many point sources of drag known as stokeslets. Finding the correct flow
field amounts to finding the set of drag forces on the stokeslets that is
consistent with the relative velocities experienced by each stokeslet. The
method rigorously satisfies the condition that the object moves with no
transfer of momentum to the fluid. We demonstrate that a sphere represented by
1999 well-separated stokeslets on its surface produces flow and drag force like
a solid sphere to one-percent accuracy. We show that a uniformly-charged sphere
with 3998 body and countercharge stokeslets obeys the Smoluchowski prediction
\cite{Morrison} for electrophoretic mobility when the countercharges lie close
to the sphere. Spheres with dipolar and quadrupolar charge distributions rotate
and translate as predicted analytically to four percent accuracy or better. We
describe how the method can treat general asymmetric shapes and charge
distributions. This method offers promise as a way to characterize and
manipulate asymmetrically charged colloid-scale objects from biology (e.g.
viruses) and technology (e.g. self-assembled clusters).
