The production cross section of a top quark pair in association with a photon is measured in proton-proton collisions in the decay channel with two oppositely charged leptons (e^±μ^∓, e⁺e^-, or μ⁺μ^-). The measurement is performed using 138 fb^-1 of proton-proton collision data recorded by the CMS experiment at √s = 13 TeV during the 2016-2018 data-taking period of the CERN LHC. A fiducial phase space is defined such that photons radiated by initial-state particles, top quarks, or any of their decay products are included. An inclusive cross section of 175.2 ± 2.5(stat) ± 6.3(syst) fb is measured in a signal region with at least one jet coming from the hadronization of a bottom quark and exactly one photon with transverse momentum above 20 GeV. Differential cross sections are measured as functions of several kinematic observables of the photon, leptons, and jets, and compared to standard model predictions. The measurements are also interpreted in the standard model effective field theory framework, and limits are found on the relevant Wilson coefficients from these results alone and in combination with a previous CMS measurement of the tt^-γ production process using the lepton+jets final state.