In this paper, for Earth-orbiting spacecraft in inclined, elliptical orbits, we present a control technique that uses a constant specific thrust (i.e., acceleration) to eliminate the rotation of the perigee that occurs due to the J2 perturbation arising from Earth's oblateness. Specifically, by averaging the rate of change of orbital elements, originating from disturbing accelerations over one orbital period, we obtain an expression that relates the secular growth of the argument of the perigee to a constant radial acceleration control. This control is used to eliminate the secular growth of the argument of the perigee due to the J2 perturbation. To justify the framework proposed in this paper, we also provide analytical expressions for the secular growth of all orbital elements caused by constant accelerations in the radial, in-plane, and out-of-plane directions. Simulation results are presented to illustrate the efficacy of the radial acceleration control in eliminating the rotation of the perigee.