A study of the charge conjugation and parity (CP) properties of the interaction between the Higgs boson and top quarks is presented. Higgs bosons are identified via the diphoton decay channel (H -> gamma gamma), and their production in association with a top quark pair ((tt) over barH) or single top quark (tH) is studied. The analysis uses 139 fb(-1) of proton-proton collision data recorded at a center-of-mass energy off root s= 13 TeV with the ATLAS detector at the Large Hadron Collider. Assuming a CP-even coupling, the (tt) over barH process is observed with a significance of 5.2 standard deviations. The measured cross section times H -> gamma gamma branching ratio is 1.64(-0.36)(+0.38)(stat)(-0.14)(+0.17) (sys) fb, and the measured rate for (tt) over barH is 1.43(-0.31)(+0.33) (stat)(-0.15)(+0.21) (sys) times the Standard Model expectation. The tH production process is not observed and an upper limit on its rate of 12 times the Standard Model expectation is set. A CP-mixing angle greater (less) than 43 (-43)degrees is excluded at 95% confidence level.