  We present a numerical code for calculating the self force on a scalar charge
moving in a bound (eccentric) geodesic in the equatorial plane of a Kerr black
hole. We work in the frequency domain and make use of the method of extended
homogeneous solutions [Phys.\ Rev.\ D {\bf 78}, 084021 (2008)], in conjunction
with mode-sum regularization. Our work is part of a program to develop a
computational architecture for fast and efficient self-force calculations,
alternative to time-domain methods. We find that our frequency-domain method
outperforms existing time-domain schemes for small eccentricities, and,
remarkably, remains competitive up to eccentricities as high as $\sim 0.7$. As
an application of our code we (i) compute the conservative scalar-field
self-force correction to the innermost stable circular equatorial orbit, as a
function of the Kerr spin parameter; and (ii) calculate the variation in the
rest mass of the scalar particle along the orbit, caused by the component of
the self force tangent to the four-velocity.
