Periodic point free homeomorphism of $T\sp 2$

Suppose that $f:{T^2} \to {T^2}$ is an orientation preserving homeomorphism of the torus that is homotopic to the identity and that has no periodic points. We show that there is a direction $\theta$ and a number $\rho$ such that every orbit of $f$ has rotation number $\rho$ in the direction $\theta$.