This work presents the results of a detailed structural characterisation of irradiated and unirradiated single crystal thin films of UO$2$. Thin films of UO$2$ were produced by reactive magnetron sputtering onto (0 0 1), (1 1 0) and (1 1 1) single crystal yttria-stabilised zirconia (YSZ) substrates. Half of the samples were irradiated with 110 MeV $\mathrm{<mrow\; data-mjx-texclass="ORD">238</mrow>}$U$\mathrm{<mrow\; data-mjx-texclass="ORD">31+</mrow>}$ ions to fluences of 5 $\times$ 10$\mathrm{<mrow\; data-mjx-texclass="ORD">10</mrow>}$, 5 $\times$ 10$\mathrm{<mrow\; data-mjx-texclass="ORD">11</mrow>}$ and 5 $\times$ 10$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$ ions/cm$2$ to induce radiation damage, with the remainder kept for reference measurements. It was observed that as-produced UO$2$ films adopted the crystallographic orientation of their YSZ substrates. The irradiation fluences used in this study however, were not sufficient to cause any permanent change in the crystalline nature of UO$2$. It has been demonstrated that the effect of epitaxial re-crystallisation of the induced radiation damage can be quantified in terms of kernel average misorientation (KAM) and different crystallographic orientations of UO$2$ respond differently to ion irradiation.