Nuclear radius of three $\alpha$ rotational state in $^{12}$C with a life time of 10$^{-21}$ second,
which has been expected to have much more extended radius than the ground $^{12}$C
nucleus, is speculated from systematic analysis of the differential cross section of the $\alpha$ + $^{12}$C
inelastic scattering. Present analysis predicts about 0.6 $\sim$ 1.0 fm enhancement in the matter radius
of the three $\alpha$ rotational state in comparison to the normal radius of the ground state.
The spatial extension of the three $\alpha$ rotational state is comparable to the extended
radius observed in the neutron halo phenomena.
Constraint on the recent ab-initio calculation for the 3$\alpha$ states in $^{12}$C is also discussed.