The process $p \bar{p}$ -> photon + jet + X as studied by the D0 detector at the Fermilab Tevatron collider at center-of-mass energy $\sqrt{s} = 1.96 \text{TeV}$. Photons are reconstructed in the central rapidity region $|y_\gamma| < 1.0$ with transverse momenta in the range 30--400 GeV, while jets are reconstructed in either the central $|y_\text{jet}| < 0.8$ or forward $1.5 < |y_\text{jet}| < 2.5$ rapidity intervals with $p_\perp^\text{jet} > 15 \text{GeV}$. The differential cross section $\mathrm{d}^3 \sigma / \mathrm{d}{p_\perp^\gamma} \mathrm{d}{y_\gamma} \mathrm{d}{y_\text{jet}}$ is measured as a function of $p_\perp^\gamma$ in four regions, differing by the relative orientations of the photon and the jet. MC predictions have trouble with simultaneously describing the measured normalization and $p_\perp^\gamma$ dependence of the cross section in any of the four measured regions.