  In the present paper we study the behavior of the normalized $I$-$Q$ relation
for neutron stars in a particular class of $f(R)$ theories of gravity, namely
the $R^2$ gravity that is one of the most natural and simplest extensions of
general relativity in the strong field regime. We study both the slowly and
rapidly rotating cases. The results show that the $I$-$Q$ relation remain
nearly equation of state independent for fixed values of the normalized
rotational parameter, but the deviations from universality can be a little bit
larger compared to the general relativistic case. What is the most interesting
in our studies, is that the differences with the pure Einstein's theory can be
large reaching above 20\%. This is qualitative different from the majority of
alternative theories of gravity, where the normalized $I$-$Q$ relations are
almost indistinguishable from the general relativistic case, and can lead to
observational constraints on the $f(R)$ theories in the future.
