Precision measurements of top-quark production with energetic photons provide a complementary probe of vector-like quarks with nonstandard radiative decays. We reinterpret the CMS differential $t\bar{t}\gamma$ measurement and the ATLAS fiducial $t\bar{t}\gamma \gamma$ cross section to constrain the electromagnetic and chromomagnetic transition interactions of a charge-$2/3$ vector-like top partner, $T$. We consider effective interactions written in terms of physical fields after electroweak symmetry breaking, retaining only the decays $T\to t\gamma$ and $T\to tg$. The CMS signal includes both the mixed $(t\gamma )(tg)$ topology and double-radiative $t\bar{t}\gamma \gamma$ events entering the exactly-one-photon fiducial region, while the ATLAS rate is interpreted using a signal-specific detector-response transfer factor. Signal uncertainties are included, and the interpretation is restricted point by point to the domain satisfying the EFT and narrow-width requirements. Denoting the electromagnetic and chromomagnetic transition coefficients by $c_{t\gamma }$ and $c_{tg}$, respectively, we find that, for $c_{tg}=1.0\times10^{-5}~\GeV^{-1}$ and $m_T=500~\GeV$, the observed Run~2 exclusions at 95% confidence level extend down to $c_{t\gamma}\simeq4.7\times10^{-7}~\GeV^{-1}$ for CMS and $2.3\times10^{-6}~\GeV^{-1}$ for ATLAS within the valid domain. At $m_T=1000~\GeV$, the corresponding values are $2.1\times {10}^{-6}$ and $8.5\times10^{-6}~\GeV^{-1}$. Projections to the HL-LHC indicate improved sensitivity to these radiative transition interactions. These results establish top-associated photon measurements as complementary probes of radiative top-partner interactions beyond searches targeting conventional decay modes.