  This paper is devoted to the existence of a weak solution to a system
describing a self-propelled motion of a rigid body in a viscous fluid in the
whole $\mathbb{R}^3$. The fluid is modelled by the incompressible
nonhomogeneous Navier-Stokes system with a nonnegative density. The motion of
the rigid body is described by the balance of linear and angular momentum. We
consider the case where slip is allowed at the fluid-solid interface through
Navier condition and prove the global existence of a weak solution.
