An analysis is presented for the steady laminar flow of an incompressible Newtonian fluid in an annulus between two concentric porous spheres with injection/suction at their boundaries. The inner sphere rotates with constant angular velocity about its own fixed axis, while the outer sphere is stationary. A solution of the Navier-Stokes equations is obtained by employing a regular perturbation technique. The solution obtained is in the form of a power series expansion in terms of the rotational Reynolds number Re, and an injection/suction Reynolds number Rew, and is valid for small values of these parameters. Results for the velocity distributions, streamlines, and viscous torques for various values of the flow parameters Re, Rew, and radius ratios λ are presented. Viscous torques at the inner and outer spheres are compared with those obtained from the numerical solution of the Navier-Stokes equations, in order to find the range of Re and Rew for which this solution is accurate.