Recent experimental results have shown that small systems such as $p$-$p$ and $p$-$A$ collisions exhibit a non-zero azimuthal anisotropy even at large $p_T$.
However, no evidence of jet quenching has been observed in these collisions.
We investigate the possibility that the azimuthal anisotropy of high-$p_T$ hadrons can be generated by the intrinsic transverse momentum of the partons in the proton.
After introducing transverse momentum dependent (TMD) parton distribution and fragmentation functions, additional polarization effects are allowed.
Unpolarized protons can generate transversely polarized quarks or linearly polarized gluons through a distribution known as the Boer-Mulders' function.
The fragmentation of similarly polarized partons to unpolarized hadrons is called the Collins' function.
We find that the high-$p_T$ azimuthal anisotropies can be obtained using these TMD distributions without modification to the angle integrated spectra.