  In this paper we study some classes of $\alpha$-attractors models in the
Jordan frame and we find the corresponding $F(R)$ gravity theory. We study
analytically the problem at leading order and we investigate whether the
attractor picture persists in the $F(R)$ gravity equivalent theory. As we show,
if the slow-roll conditions are assumed in the Jordan frame, the spectral index
of primordial curvature perturbations and the scalar-to-tensor ratio are
identical to the corresponding observational indices of the $R^2$ model, a
result which indicates that the attractor property is also found in the
corresponding $F(R)$ gravity theories of the $\alpha$-attractors models.
Moreover, implicit and approximate forms of the $F(R)$ gravity inflationary
attractors are found.
