The cross section for inclusive production of $f_2(1270)$ meson
is calculated. We include both the mechanism of gluon-gluon fusion
as well as the $\pi \pi$ final-state rescattering.
The contribution of the gluon-gluon fusion is calculated within
the $k_t$-factorization approach with modern unintegrated gluon
distribution functions (UGDFs).
Some parameters for the $g^* g^* \to f_2$ vertex are extracted from
the $\gamma \gamma \to f_2(1270) \to \pi \pi$ reactions.
The results strongly depend on the parametrization of the
$g^* g^* \to f_2(1270)$ form factor.
Results of our model are compared to the ALICE preliminary data.
The gluon-gluon fusion does not explain low-$p_t$ data but could
be the dominant mechanism at somewhat larger meson transverse
momenta.
By adjusting some parameters the pion-pion rescattering can explain
the low-$p_t$ region.